He announced his decision in Moscow after accepting more than $2bn in Russian aid and credit.
The US base, outside the Kyrgyz capital Bishkek, had been set up to assist international forces in Afghanistan.
However, Kyrgyzstan's government has long been unhappy over its prolonged presence.
Under the terms of the original deal Washington has six months to shut down the base after being informed that Kyrgyzstan no longer wishes it to remain.
Following Kyrgyzstan's announcement, Russia said it would allow non-lethal US military supplies for Afghanistan to cross its territory.
David Petraeus, the commander of US forces in Afghanistan and Iraq, visited Uzbekistan, Kyrgyzstan's neighbour, on Tuesday in an attempt to secure alternative supply routes into Afghanistan for US forces.
Convoys travelling along Pakistani supply lines to Nato and US-led troops in Afghanistan have been attacked and the closure of the Manas base could cause further logistical problems.
Barack Obama, the US president, has approved the deployment of an extra 17,000 troops to Afghanistan.