The head of the election commission in the strategically located Caucasus nation, Zurab Chiaberashvili, said in televised comments that Saakashvili had obtained 62% of all votes cast in Sunday's ballot.
Saakashvili needed 50% of the votes plus one to win.
"Saakashvili has won," Keti Korinteli, a spokeswoman for the central election commission, told AFP. "It was clear already and now it is even more so."
Chiaberashvili said that with 63% of ballot papers counted, Saakashvili had obtained 1,096,349 of the 1,761,936 votes cast.
He is not expected to be officially declared the victor until all ballot papers are counted.
His inauguration has tentatively been scheduled for 25 January, which ironically falls on the 76th birthday of the man he drove from power - Shevardnadze, the former Soviet foreign minister who helped end the Cold War and dominated political life in Georgia for decades.
Saakashvili spearheaded the mass protests over a disputed parliamentary election that peacefully ousted Shevardnadze in Georgia's "rose revolution" at the end of November 2003.
Saakashvili and many of the protestors brandished roses as they stormed parliament in the revolution's climax, to symbolise the peaceful nature of the demonstrations.
The overwhelming support Saakashvili mustered in Sunday's vote reflects a widespread hope in Georgia that the energetic firebrand can do something about the corruption, poverty and separatism that have plagued the country since the breakup of the Soviet Union.
But Saakashvili faces daunting problems as he takes over the helm of one of Europe's most dysfunctional states.
Supporters of Saakashvili
celebrate his victory
The government is broke, corruption is endemic, Georgia's infrastructure is in tatters and two regions, Abkhazia and South Ossetia, are controlled by separatist rebels.
Saakashvili has said his priorities will be to wage war on corruption, rescue the economy, bring separatist territories back under control, embrace Europe and the United States and mend fractious relations with neighbouring Russia.
His first steps as president will be watched closely by both Russia and the United States, rivals for influence over the small but strategically important country.
Georgia is a crossroads for the export of crude oil from the massive new fields of the Caspian Sea to international markets.
Analysts warn Saakashvili's pledge to restore central control over separatist regions could set him on a collision course with Moscow, which backs the regions and is wary of his pro-Western leanings.
Sunday's election was billed by the international community as a test of Georgia's new rulers' democratic credentials and, judging by initial reactions, it appeared to have passed muster.
Authorities "showed the political will to conduct democratic elections"
Organisation for Security and Cooperation in Europe (OSCE)
Observers from the Organisation for Security and Cooperation in Europe (OSCE) said the authorities "showed the political will to conduct democratic elections" and both the European Union and the United States hailed the poll as an important step for Georgian democracy.
Saakashvili, who speaks fluent French and English as well as Georgian, Russian and Ukrainian, studied at Columbia University law school in the United States and briefly served as a minister in Shevardnadze's government before quitting to form his own opposition party.