The leaders, meeting in Ghana, agreed to send a vanguard of 1,500 peacekeepers, expected to be two battalions from Nigeria.
The pledge came as pressure grew on regional leaders to speed a peace force promised since rebels opened two months of bloody siege on Liberia's capital in early June.
Aid groups say more than 1,000 civilians have been killed and tens of thousands driven from the homes.
Mohamed Ibn Chambas, executive secretary of the West African leaders' bloc, said the vanguard force would provide the "appropriate conditions for the handover of power, and departure from Liberia, of President Charles Taylor."
Earlier Thursday, Monrovia's trapped people welcomed an advance team scouting conditions for the long-promised West African peace force.
With the new hopes of rescue, people in Liberia's capital passed one of the quietest nights in the last two months of rebel offensives. Gunfire rattled, but there was relief from the rocket and mortar volleys of recent days.
The advance team of West African and U.S. officials, which is led by a Nigerian commander, set off jubilant celebrations in Monrovia as it passed shacks with tin roofs peeled back by explosives and undetonated shells in the streets.
"This is a sign of peace coming," refugee Hamilton Woods said with a smile.
In a statement, the leaders said "it was agreed" that Taylor would hand over power to a successor, and accept an offer of exile in Nigeria, within three days of the troops' arrival.
Taylor, a wanted U.N. war-crimes suspect for his backing of rebels in the neighboring nation of Sierra Leone, has said in recent weeks that he would yield power as soon as peace troops arrive.
It was not clear whether West African leaders had specifically won Taylor's agreement on their announcement. Liberian officials in Monrovia could not immediately be reached for comment.
West African leaders have promised for weeks to send peacekeepers to Liberia's capital, where rebels are pressing home a 3-year-old war to oust Taylor. Fighting has isolated Monrovia, cutting off food and clean water to the city of more than 1.3 million and raising the threat of disease and starvation.
Taylor, a former warlord, has presided over 14 years of near perpetual conflict in Liberia, once one of West Africa's most prosperous nations.
On Wednesday, U.N. Secretary-General Kofi Annan had urged West African leaders to commit to a date for the peace force.
Debt-plagued Nigeria, which will form the advance force, asked the United States and others for more help with what's expected to be a multimillion-dollar daily tab.
The United States, which oversaw founding of Liberia by freed American slaves in the 19th century, has promised $10 million and is sending three warships with Marines to Liberia for what President Bush says will be limited assistance.
U.S. officials introduced a draft measure at the United Nations on Wednesday asking for approval of a multinational force, to be followed by Oct. 1 by a U.N. deployment.
In Monrovia, tens of thousands of Liberians emerged from hiding places to welcome a West African-U.S. advance team they hoped signaled the imminent arrival of peacekeepers.
Nigeria, Ghana, Mali, Benin, Senegal and Togo have promised 3,250 soldiers for an eventual 5,000-strong force.