Giorgi Margvelashvili, a politically inexperienced academic from Ivanishvili's Georgian Dream coalition, was cantering to victory with some 62 percent of the vote at the election Sunday after ballots from over 70 percent of polling stations had been tallied, the election commission said.
His nearest challenger, ex-parliament speaker David Bakradze from Saakashvili's United National Movement party, trailed behind on just under 22 percent, official results showed.
Margvelashvili had already hailed victory before cheering supporters at a rally in the capital Tbilisi Sunday after exit polls indicated he was cruising the presidency.
"I thank you all so much. It is our shared victory," Margvelashvili said as balloons were released to chants from the crowd.
Savouring the win, Georgia's richest man Ivanishvili said at the rally that his coalition would aim to work with its opponents.
"All together we will build a Georgia which we dream about," Ivanishvili said. "I congratulate you all."
Fireworks exploded over the capital after polls closed in the Caucasus republic of some 4.5 million, as convoys of Margvelashvili supporters beeped car horns and waved flags.
Runner-up Bakradze was quick to admit he had lost.
"I congratulate Giorgi Margvelashvili on his electoral win and the trust expressed in him by the Georgian people," Bakradze said in televised comments.
He said the vote confirmed Saakashvili's UNM party as the main opposition in the country, with partial results giving combative ex-parliament chairwoman Nino Burjanadze just over 10 percent in third place.
Sunday's vote calls time on US ally Saakashvili's decade in power and his bitter year-long cohabitation with bete noire Ivanishvili, who has promised to also step down in the coming weeks.
In a televised address, Saakashvili urged his supporters to respect the outcome of the poll even though he called it a "serious deviation" from Georgia's path towards development.
"The Georgian voters have expressed their will. I want to tell those who are not happy with the results: we must respect the majority's opinion," Saakashvili said, standing on a podium lined with Georgian flags.
If confirmed, Margvelashvili will assume a weakened role as constitutional changes will see the next president cede many key powers to the prime minister.
The lower stakes meant that voting was at a trickle throughout Sunday and the final turnout was just 46.6 percent, according to the election commission.
Commission chairwoman Tamar Zhvania said in a statement early Monday that there were no major violations and that the poll saw "voters freely expressed their will".
Ivanishvili, 57, wrested power from Saakashvili's party at parliamentary polls last year, heralding Georgia's first smooth handover of power.
Supporters said Margvelashvili, a knitting-loving former philosophy lecturer who owes his meteoric rise to Ivanishvili, represented the polar opposite of Saakashvili.
"We don't need another emotional and headstrong president," Serge Tsutskiridze, a univerity professor, said after voting.
'Open and transparent vote'
US ambassador to Georgia Richard Norland said the vote seemed to be going smoothly as he toured polling stations Sunday.
"What's important is that this vote proceeds today in a way that's peaceful, fair, open and transparent and, so far, things seem to be moving in that direction."
Transparency International said however the number of procedural violations was up on last year's vote.
Georgia under Saakashvili made joining NATO and the European Union a main priority, and Margvelashvili has pledged to press on with that drive.
He has also promised to try to mend ties with Moscow shattered by a brief 2008 war that saw Georgia effectively lose two breakaway regions.
Western allies have expressed concern over perceived selective justice that has seen a string of Saakashvili's close allies arrested since his party lost power.
Saakashvili has said he wants to remain active in politics but Ivanishvili, whose coalition will retain control of the government, has labelled him a "political corpse" and warned that he could face prosecution.
During a turbulent decade, Saakashvili -- who came to power after ousting Eduard Shevardnadze in the 2003 "Rose Revolution" -- cut corruption, built new infrastructure and revived Georgia's economy.
But his reforms angered many who felt left out by the rush to change, while police brutality used in crushing opposition protests tarnished his image as a pioneering democrat.