Annan met al-Asad on the sidelines of an Arab summit in Algiers on Tuesday and said the Syrian president confirmed his commitment to UN Resolution 1559, which called for a total Syrian withdrawal.
"The withdrawal has begun and it continues. He's working out a timetable in consultation with the Lebanese authorities and will withdraw his troops completely into Syrian territory. Not just the troops but also the security service, as well as all the logistical and material equipment to Syria," Annan said.
Syria has pulled back its troops and intelligence agents into eastern Lebanon towards the border and has been promising to work out their complete removal with the pro-Syrian government in Beirut.
Annan said al-Asad agreed to have a schedule ready in time for a visit to Damascus by a UN envoy in the first week of April. The secretary-general said he expected the envoy to return with a "credible and well-defined timetable".
"We need to see all of them withdrawn and President Asad has confirmed to me that this is his intention and he will implement 1559 in full," Annan said. "We are going to work with him to ensure that it is done."
In the pullback over recent weeks, Syria says 4000 of its 14,000 troops have left Lebanon completely. The remaining are in the Bekaa Valley in eastern Lebanon.
"We need to see all of them withdrawn and President Asad has confirmed to me that this is his intention and he will implement 1559 in full"
UN Secretary-General Kofi Annan
The US, France and the UN have stepped up pressure on Syria for total withdrawal of its troops before Lebanese elections scheduled for May.
Syria had sent troops to Lebanon in 1976 to keep peace during a civil war. The war ended in 1990, but Damascus left some of its troops inside Lebanon, helping it to keep a grip over Lebanese political affairs.