Georgy Margvelashvili's triumph concentrates power and will make policy-making easier in the former Soviet republic because Ivanishvili's Georgian Dream coalition now controls both the presidency and the government for the first time.
Exit polls showed the margin of victory was so large that the candidate from Saakashvili's party, David Bakradze, conceded victory to Margvelashvili even before the official count began.
Georgian Dream supporters released dozens of balloons in the coalition's blue and white colours outside its headquarters in the capital Tbilisi, sounded car horns in the packed streets and chanted: "Long live Georgy".
"We have shown the world how free people make a free choice," Margvelashvili, a 44-year-old former vice premier with a doctorate in philosophy, told cheering supporters.
He wrapped his arm around the shoulders of Ivanishvili, who plucked him out of academia when Georgian Dream ousted Saakashvili's government at the polls a year ago, and praised him as the "biggest authority" in the South Caucasus country.
Margvelashvili had needed one vote over 50% of the ballots cast to secure victory without a run-off. GfK, a European market research group, put him on 66.1% and ACT, a Georgian research group, estimated he would win 68%.
But the election is likely to provide only a brief respite from political uncertainty in the country of 4.5 million which is strategically important for both Russia and Europe, which gets Caspian gas and oil via pipelines that go through Georgia.
Prime Minister to step aside
Ivanishvili, Georgian Dream's founder and the most powerful and richest man in Georgia with an estimated fortune of $5.3 billion (€3.8 billion), says he will step aside soon because his job will be complete when his 45-year-old rival leaves the presidency.
He has not said who will be the next prime minister - the most important job in Georgia under constitutional changes that are about to go into effect - or how he might continue to bring influence to bear on the coalition from the sidelines.
The European Union is also worried by the arrest of several former ministers and other officials, including a former prime minister, and that Saakashvili could suffer the same fate.
Georgians are openly speculating that Saakashvili might soon leave the country to avoid prosecution.
He went on television soon after voting ended to say he was worried about Georgia's immediate future. But, echoing his decision to quickly concede victory to Georgian Dream after last year's parliamentary election to ease tension, he sought calm.
"I think the events of the past year and today, and the results today, are a serious setback for Georgia and its future," he said. "But at the same time I am sure the dark forces will not be able to get any stronger and that Georgia has a good future."
Poverty remains a problem and, after years of robust growth, gross domestic product grew 1.5% in the second quarter this year, down from 8.2% in the same period a year ago.
Margvelashvili owes his rise to Ivanishvili's patronage and his lack of political experience may have helped him in a country where voters are weary of squabbling among politicians.
"He is a new type of politician, a new generation," Gogi Popkhadze, 35 and unemployed, said as he voted for Margvelashvili in bright sunshine in Tbilisi.
Margvelashvili's main foreign policy goal is to pursue close ties with both the West and Russia, a balance that has long eluded Georgia.
Saakashvili strengthened democracy and launched economic reforms after coming to power following the bloodless "rose revolution" in 2003 that ousted Eduard Shevardnadze.
He strengthened ties with Washington and became a Western darling but lost a brief war to Russia in 2008 over two rebel Georgian regions and failed to reform the justice system.