Russian Foreign Minister Sergey Lavrov said on Monday the withdrawal - which would be completed over the course of 2008 - would take place "without any kind of discomfort for the soldiers" and added the pact would "help further develop our relations".
The agreement was "an important and constructive step", Lavrov's Georgian counterpart, Salome Zurabishvili, said at a news conference at Georgia's embassy in Moscow.
"We have achieved the goal which we have long been working for."
Lavrov said troops and equipment would be withdrawn first from the military base at the southern city of Akhalkalaki and then from the Black Sea port of Batumi.
About 3000 troops are stationed at the two bases, which are holdovers from the Soviet era; two others were closed over the past decade.
Russia commits itself to start withdrawing - beginning mainly with heavy equipment - this year, according to the agreement, whose text was posted on the Russian Foreign Ministry website.
Zurabishvili said a formal agreement would have to be signed and ratified by Russia's parliament in order for Russia to allocate funds to close the bases.
The deal is a victory for Georgian President Mikhail Saakashvili, who has sought to move his country out of the shadow of its giant neighbour and towards deeper economic and military relations with the US and Europe.
The full Russian troop withdrawal
will be completed by 2008
Zurabishvili said the base dispute "is only one of the issues we have in Georgian-Russian relations".
"This agreement doesn't mean we have solved everything," she said.
But she claimed it was a good start, and that, if managed correctly, it could build trust "instead of becoming a process for humiliation or failure".