“City hall is almost completely evacuated,” opposition spokesman Ruslan Andriyko told AFP.
The government had promised to drop all charges against demonstrators if they vacate government buildings and lift roadblocks by Monday.
City hall has been occupied by protesters for more than two months.
The protests started in November when President Viktor Yanukovych abandoned plans to sign a far-ranging association agreement with the EU.
Instead, Viktor Yanukovych 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 Organization for Security and Cooperation in Europe.
On Friday authorities released the last of 243 prisoners who were arrested during the unrest.
Viktor 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.
Yulia Tymoshenko went to accuse President Viktor Yanukovich of being under the control of Russia’s Vladimir Putin, his major international backer.
nCSVKQ6ZamoImage source: Wikimedia Commons President-elect Donald Trump celebrated his election victory at the Ultimate Fighting…
Millions of voters across the US chose to return Donald Trump to the White House…
Donald Trump declares victory in the US election as he addresses jubilant supporters in Florida.…
Stocks around the world are rising as Donald Trump appears to be on the cusp…
Donald Trump has won Pennsylvania, North Carolina and Georgia and taken a lead over Kamala…
Quincy Jones, the celebrated musician and producer who worked with Michael Jackson, Frank Sinatra, Ray…