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The deal provides for a national unity government, electoral reform and constitutional changes reducing the president's power.
The compromise came after hours of talks, mediated by three European Union foreign ministers.
The German and Polish foreign ministers met protest leaders, who later announced that they backed the deal.
Polish Foreign Minister Radoslaw Sikorski tweeted that the deal was a "good compromise for Ukraine" which would open the way "to reform and to Europe".
UK Prime Minister David Cameron also welcomed the agreement and called on all sides in Ukraine to "get behind this deal and deliver it according to the timetable set out".
Tymoshenko vote Shortly after the deal was signed, Ukraine's parliament approved the restoration of the 2004 constitution, with all but one of the 387 MPs present voting in favour.
Mr Yatsenyuk said the vote was "the first step to restore order in Ukraine".
Parliament also approved an amnesty for protesters accused of involvement in violence and voted for the dismissal of Interior Minister Vitaliy Zakharchenko.
Despite the agreement, isolated outbursts of violence were reported in central Kiev on Friday morning.
The police said they had traded gunfire with protesters, and Ukrainian media said riot police were patrolling inside parliament during a session.
It remains to be seen whether the deal will be enough to placate more radical elements of the opposition, including many in the west of Ukraine, who have been demanding Mr Yanukovych's resignation.
MPs once again began the session with scuffles, as the speaker tried to adjourn a debate about constitutional reform.
The protests first erupted in late November when President Yanukovych rejected a landmark association and trade deal with the EU in favour of closer ties with Russia.
Mr Yanukovych (centre), opposition
leaders and Polish Foreign Minister Radoslaw Sikorski (far right)
observed a moment's silence at the signing for those who had died in
recent violence
Protesters began rebuilding barricades in the Maidan (Independence Square) early on Friday
The stand-off continues as opposition leaders discuss tactics with their colleagues, a day after dozens were shot by police
Protesters are once again occupying official buildings, days after vacating them
The deal comes after the bloodiest day since the unrest began.
Police opened fire early on Thursday after protesters tried to push them away from the makeshift camps they have been occupying in central Kiev.
The health ministry said 77 people had been killed since Tuesday, and another 577 were injured.
But activists suggested the death toll was likely to be much higher.
On Friday the US state department issued a travel warning advising its citizens to "defer non-essential travel" to Ukraine, saying that it had authorised "the departure of all family members of US government personnel from Ukraine".
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Baroness Ashton: "President Yanukovych has now staked himself on this"
Ukrainian
President Viktor Yanukovych and opposition leaders have signed a deal
leading to an early presidential poll before the end of the year.
The election is part of an agreement to end the country's political crisis.The deal provides for a national unity government, electoral reform and constitutional changes reducing the president's power.
The compromise came after hours of talks, mediated by three European Union foreign ministers.
The German and Polish foreign ministers met protest leaders, who later announced that they backed the deal.
Continue reading the main story
But the problems facing Ukraine's leaders are formidable. On the political front they must rewrite the constitution, switch power from the president to parliament and then stage new elections. They must also find ways of dealing with groups pressing for secession. On paper, it sounds easy. In reality, it will be a messy business, the outcome uncertain.
Alongside the political changes is the challenging task of reforming the police and dismantling the whole apparatus of repression. Corrupt prosecutors and judges will have to be replaced.
And then there's the economy. The Ukrainian currency, the hryvnya, has tumbled in value. There's a shortage of petrol, bread and even cash. International ratings agencies have warned of the country defaulting on its debts.
Ukraine cannot survive without help - but where should it come from? Russia has promised a $15bn (£9.2bn; 10.9bn euros) loan - lent in dribs and drabs. Now the EU has woken up to the importance of Ukraine, the question is whether this union of 27 is going to commit to a multibillion-pound bailout package of its own for just a single country - one which may join the EU one day, but not soon.
Analysis
The primary aim of any new government - which could be in place with a week or two - will be to restore peace and political stability to a country that has been on the brink of civil war.But the problems facing Ukraine's leaders are formidable. On the political front they must rewrite the constitution, switch power from the president to parliament and then stage new elections. They must also find ways of dealing with groups pressing for secession. On paper, it sounds easy. In reality, it will be a messy business, the outcome uncertain.
Alongside the political changes is the challenging task of reforming the police and dismantling the whole apparatus of repression. Corrupt prosecutors and judges will have to be replaced.
And then there's the economy. The Ukrainian currency, the hryvnya, has tumbled in value. There's a shortage of petrol, bread and even cash. International ratings agencies have warned of the country defaulting on its debts.
Ukraine cannot survive without help - but where should it come from? Russia has promised a $15bn (£9.2bn; 10.9bn euros) loan - lent in dribs and drabs. Now the EU has woken up to the importance of Ukraine, the question is whether this union of 27 is going to commit to a multibillion-pound bailout package of its own for just a single country - one which may join the EU one day, but not soon.
The agreement, published by the German foreign ministry, includes the following:
- The 2004 constitution will be restored within 48 hours, and a national unity government will be formed within 10 days
- Constitutional reform balancing the powers of president, government and parliament will be started immediately and completed by September
- A presidential election will be held after the new constitution is adopted but no later than December 2014 and new electoral laws will be passed
- An investigation into recent acts of violence will be conducted under joint monitoring from the authorities, the opposition and the Council of Europe
- The authorities will not impose a state of emergency and both the authorities and the opposition will refrain from the use of violence
- Illegal weapons will be handed over to interior ministry bodies
Polish Foreign Minister Radoslaw Sikorski tweeted that the deal was a "good compromise for Ukraine" which would open the way "to reform and to Europe".
UK Prime Minister David Cameron also welcomed the agreement and called on all sides in Ukraine to "get behind this deal and deliver it according to the timetable set out".
Tymoshenko vote Shortly after the deal was signed, Ukraine's parliament approved the restoration of the 2004 constitution, with all but one of the 387 MPs present voting in favour.
Mr Yatsenyuk said the vote was "the first step to restore order in Ukraine".
Parliament also approved an amnesty for protesters accused of involvement in violence and voted for the dismissal of Interior Minister Vitaliy Zakharchenko.
Continue reading the main story
Any political deal between President Yanukovych and the
opposition movement will have to pass the test here in Lviv. It is a
city that has been at the forefront of the protests, sending busloads of
demonstrators 500km east to Kiev on a nightly basis.
Lviv has always looked west rather than east: a city for centuries under Austrian and then Polish rule only fell to the Soviets during World War Two and has remained fiercely proud of its Ukrainian identity ever since.
The writ of the Kiev government does not extend here. Every regional administration building is now under the control of the protest movement. I visited the police headquarters, taken on Tuesday night by the opposition and ransacked. At the security service office, burnt out cars lie in the courtyard.
The mood here is one of defiance: that President Yanukovych must step down now. This pro-Western part of Ukraine is determined that its voice will be heard.
At the scene
Lviv has always looked west rather than east: a city for centuries under Austrian and then Polish rule only fell to the Soviets during World War Two and has remained fiercely proud of its Ukrainian identity ever since.
The writ of the Kiev government does not extend here. Every regional administration building is now under the control of the protest movement. I visited the police headquarters, taken on Tuesday night by the opposition and ransacked. At the security service office, burnt out cars lie in the courtyard.
The mood here is one of defiance: that President Yanukovych must step down now. This pro-Western part of Ukraine is determined that its voice will be heard.
MPs voted for a change in the law
which could lead to the release of jailed former Prime Minister Yulia
Tymoshenko, an arch-rival of Mr Yanukovych.
She was sentenced to seven years in prison in 2011 for abuse
of power. Her supporters say this was simply Mr Yanukovych taking out
his most prominent opponent.Despite the agreement, isolated outbursts of violence were reported in central Kiev on Friday morning.
The police said they had traded gunfire with protesters, and Ukrainian media said riot police were patrolling inside parliament during a session.
It remains to be seen whether the deal will be enough to placate more radical elements of the opposition, including many in the west of Ukraine, who have been demanding Mr Yanukovych's resignation.
MPs once again began the session with scuffles, as the speaker tried to adjourn a debate about constitutional reform.
The protests first erupted in late November when President Yanukovych rejected a landmark association and trade deal with the EU in favour of closer ties with Russia.
Mr Yanukovych (centre), opposition
leaders and Polish Foreign Minister Radoslaw Sikorski (far right)
observed a moment's silence at the signing for those who had died in
recent violence
Protesters began rebuilding barricades in the Maidan (Independence Square) early on Friday
The stand-off continues as opposition leaders discuss tactics with their colleagues, a day after dozens were shot by police
Protesters are once again occupying official buildings, days after vacating them
Police opened fire early on Thursday after protesters tried to push them away from the makeshift camps they have been occupying in central Kiev.
The health ministry said 77 people had been killed since Tuesday, and another 577 were injured.
But activists suggested the death toll was likely to be much higher.
On Friday the US state department issued a travel warning advising its citizens to "defer non-essential travel" to Ukraine, saying that it had authorised "the departure of all family members of US government personnel from Ukraine".