"President Taylor will leave Liberia after the installation of that vice-president on Monday," Mbeki told reporters after meeting visiting Kenyan President Mwai Kibaki in Pretoria.
Taylor would travel to Nigeria, which has granted him asylum if he relinquishes power.
Mbeki said Taylor called him on Monday to declare his intention of stepping down to make way for a government of national unity to be led by Vice-President Moses Blah.
"President Taylor will leave as soon as possible after that - either that same day or a day after - to go to Nigeria".
The first battalion of Nigerian troops arrived in Monrovia on Monday, spearheading the deployment of a West African force in a bid to end a decade of civil war in Liberia.
More troops from the region are expected to arrive within the few days.
The peacekeeping force is expected to ultimately number between 3 000 and 5 000 men, who will be commanded by Nigerian General Festus Okonkwo.
Mbeki said: "So within the next ten days there will be a substantial force in Liberia and a new government of national unity that will include rebel groups fighting now".
This would hopefully bring peace to Liberia and create conditions to prepare for elections and to disarm the various militia, Mbeki said.
Warlord-turned-president Taylor has made earlier promises to step down, but doubts have been lingering about his intention to leave the country.
His government said on Saturday Taylor would leave Liberia only once a sufficient number of peacekeepers were deployed and if no war-crime charges were brought against him.
Both the Taylor government and the rebel movement Liberians United for Reconciliation and Democracy (Lurd) have promised to work with the peacekeepers.
But both camps have violated earlier ceasefire agreements.
On Sunday, new clashes were reported in Buchanan, Liberia's second city, between government troops and rebel fighters.
Fighting since early June has claimed more than 1 000 civilian lives in Monrovia, a city now crowded with hundreds of thousands of refugees short of food and water.
Mbeki said yesterday he and Kibaki also discussed other African trouble spots, including the Sudan, Somalia and Burundi.
Kenya is leading negotiations to seek a peaceful settlement for the conflict in the Sudan and Somalia.
"We looked at those and we hope there will be movement to solve these questions as soon as possible," Mbeki said.
He said he briefed Kibaki on the progress of peace efforts in the Democratic Republic of Congo and Burundi.
Negotiations in Burundi, facilitated by Deputy President Jacob Zuma, would hopefully be concluded this week.
"We hope all outstanding questions will be resolved so that we can implement the entirety of the agreement on Burundi".
These developments and Taylor's undertaking to step down gave rise to some optimism.
"Generally, there is forward movement on the continent with regard to addressing these conflict areas. I think that is a very hopeful sign for the continent," Mbeki said. – Sapa.
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