Shevardnadze confirmed on state television that he had signed his resignation papers and said he is "going home."
Crowds of opposition protesters are celebrating outside Georgia's parliament building, whistling, cheering, waving flags, and lighting firecrackers.
The opposition has described the protests as a "bloodless, velvet revolution."
Shevardnadze held talks with Russian Foreign Minister Igor Ivanov and opposition leader Mikhail Saakashvili.
The meeting, at the president's residence on the outskirts of Tbilisi, came shortly after Saakashvili called on supporters to march on the president's residence unless he resigns, also saying it was "too late" for talks.
Shevardnadze earlier said he was ready to discuss holding early presidential elections and restaging a disputed parliamentary poll if opposition supporters left the parliament building.
Opposition protesters stormed the Georgian Parliament November 22 after weeks of protests demanding Shevardnadze's resignation over November 2 parliamentary elections, which the opposition, international monitors, and the United States say were marred by fraud.