The pullback would be the biggest single such move since Syrian forces intervened in Lebanon's civil war in 1976.
It has some 14,000 troops there, down from 40,000.
Syrian President Bashar al-Assad agreed the withdrawal plan in talks with his Lebanese counterpart Emile Lahoud in Damascus, a statement said.
The Syrian troops will complete their move to eastern Lebanon by March 31, the statement said. The Syrian and Lebanese military will then decide how long the Syrians stay there.
The plan means Syrian troops will be gone from most, but probably not all, of Lebanon before general elections due by May.
The United States has demanded the departure of all Syrian troops and intelligence agents before the poll.
Germany, France and Britain urged Syria to move swiftly.
"We expect Syria to withdraw its troops and security services completely and as quickly as possible," German Chancellor Gerhard Schroeder and French President Jacques Chirac said in a joint statement.
British Foreign Secretary Jack Straw said Syria's move was welcome as a "first step" and that "we expect to see rapid progress to the withdrawal of Syrian troops from the whole of Lebanon", in line with a UN resolution last year.
Even while Mr Assad and Mr Lahoud were meeting, Syrian soldiers based in the Lebanese mountain towns of Hamana, Mdairij, Soufar and Aley, were dismantling communications equipment or loading military gear and belongings on to army trucks, witnesses said.
Some trucks with equipment and a few dozen soldiers from several posts headed eastwards. Other troops stayed behind.
Lebanese army soldiers waited in trucks near a Syrian military post at Dahr al-Wahsh, east of Beirut, as the Syrian troops prepared to leave.
Syria's role in Lebanon has come under fierce fire since a February 14 bombing that killed former Lebanese prime minister Rafik al-Hariri.
Damascus denied any involvement in the blast.
Thousands of Lebanese flag-waving protesters again took over central Beirut's Martyrs Square chanting "freedom, sovereignty, independence" and demanding Syria quit Lebanon completely.
Some of the youthful crowd were supporters of exiled general Michel Aoun, a staunchly anti-Syrian Maronite Christian, who dismissed the Syrian withdrawal plan as stalling tactics.
"I don't think Assad will respect his commitments and it will not be the first time," Mr Aoun said in Paris.
"He is manoeuvring to win time. "He doesn't want to withdraw.
"He still hopes to make some changes in international policy but I think he's heading for a confrontation with the international community," Mr Aoun said.
Mr Assad and Mr Lahoud said they respected UN Security Council resolutions, including one demanding that Syria quit Lebanon, as well as the Taif Accord, which ended Lebanon's civil war and which envisaged a Syrian pullout from most parts of the country. Syria has previously said compliance with the Taif Accord amounts to fulfilling the UN resolution adopted in September.
Mr Aoun, driven from east Beirut by the Syrians in 1990 with the tacit approval of the US, rejected Taif at the time because it did not guarantee a full Syrian withdrawal.
On Saturday Mr Assad promised a troop pullback, but declared Damascus would still play a role in its much smaller neighbour.
Lebanon's most powerful and only armed party, Hizbollah, has called for peaceful protests today in support of Syria and warned of mayhem if Syrian troops were to leave.
Set up by Iran's Revolutionary Guard in 1982, Shi'ite Muslim Hizbollah is the only Lebanese faction to keep its guns.
It gained wide popularity after helping drive Israeli troops from south Lebanon in 2000.
Washington says it is a terrorist group.