Protesters unhappy with President Yanukoych's ditching of an agreement with the EU have held the building for more than two months.
Officials promised to drop charges against demonstrators if they left all government buildings by Monday.
Protest leaders say they have now fulfilled the government's conditions for an amnesty.
The BBC's David Stern in Kiev says protesters have also partially dismantled barricades on a street in central Kiev.
The protests started in November when President Viktor Yanukovych abandoned plans to sign a far-reaching association agreement with the EU.
Instead, he advocated closer trade relations with Russia, which dominated Ukraine for centuries until the fall of the Soviet Union in 1991.
People began walking out of the building on Sunday morning.
The Swiss ambassador in Kiev entered the building soon afterwards in order to help transfer the building to the control of the authorities.
Switzerland currently holds the rotating presidency of the Organisation for Security and Cooperation in Europe.
On Friday authorities released the last of 243 prisoners who were arrested during the unrest.
Mr Yanukovich passed an amnesty law earlier this month and agreed to negotiate with the opposition after at least four people were killed in protests.
This weekend, some opposition members continued to call for his departure, and another demonstration is due to place in Kiev's central Independence Square.
"The only subject of negotiation with Yanukovych is the conditions of his departure," jailed opposition leader Yulia Tymoshenko said on Saturday.
She went to accuse the Ukrainian president of being under the control of Russia's Vladimir Putin, his major international backer.
Source: BBC News