The group, which included the Soros Foundation, the British Council and other international groups, said: "According to the results of the exit poll, the election was won by Mikhail Saakashvili".
Claiming victory, Saakashvili hailed the election as a victory for the Georgian people.
There were six names on Sunday's ballot paper but Mikhail Saakashvili, a 36-year-old reformer with pro-Western leanings, was the overwhelming favourite to take the top job in the impoverished and chaotic former Soviet republic.
His victory sets the seal on a tumultuous fortnight in November when he led mass protests which harried into retirement 75-year-old Shevardnadze, best known in the West for helping end the Cold War as Soviet foreign minister.
Saakashvili was already looking ahead to taking office Sunday.
"I am thinking about what concrete steps I can take to make life better than it has been up to now," he said as he cast his vote in the capital, Tbilisi.
The outcome of the election was being watched closely by both Russia and the US, rivals for influence over the small but strategically-important country.
Georgia is at the crossroads of export routes for crude oil from the massive new fields of the Caspian Sea to international markets.
Sunday's election was also being scrutinised by the international community for evidence that the country's new leaders will be true to their word and turn their back on the fraudulent elections of the past.
The frontrunner got an unlikely endorsement earlier Sunday from his foe Shevardnadze.
Shevardnadze says he voted for
the man who forced him out
The former president said he had voted for Saakashvili. But there was a sting in the tail, with a warning for the upstart, who has a reputation as a firebrand: "He should talk less and work more. Enough of populism. There is a lot to be done."
Saakashvili, who has a Dutch wife and speaks fluent French, English, Georgian and Russian, as well as Ukrainian, studied at Columbia University law school in the US and briefly served as a minister in Shevardnadze's government.
He quit and joined the opposition, and when a 2 November parliamentary election was widely deemed to have been rigged by the government, he spearheaded weeks of mass protests on the streets of Tbilisi.