As of early Tuesday, Susilo had yet to claim victory after Monday's run-off, but he had won 60% of the ballots counted, while Indonesian President Megawati Sukarnoputri had garnered 40%.
In past elections, early counting has proved a reliable guide to final results and pre-election polls as well as an independent survey of Monday's vote also forecast a Susilo victory.
About 56 million votes had been counted by early Tuesday. About 80% of the 153 million registered voters had cast their ballot, officials said.
Indonesia's financial markets strengthened on Tuesday after the peaceful conclusion to a long election season in the world's most populous Muslim nation, and on expectations the market-friendly Susilo, 55, will appoint a strong cabinet.
The stock market hit an intra-day record in early trade before losing some gains on profit taking, while the rupiah currency was trading at about 8990 to the dollar, above Monday afternoon levels of just over 9000.
Susilo declined to formally claim victory late on Monday, but thanked the people of Indonesia for supporting him.
Megawati, 57, who had stabilised the economy but saw her popularity wane because of anger over continuing graft, did not concede, saying she would await the announcement of official results in early October.
Megawati says she will wait for
official results out in October
Susilo has already reached out to Megawati who in public has barely acknowledged him since he quit her cabinet as chief security minister in March after a bitter row over his presidential ambitions.
"It is time for reconciliation," Susilo said late on Monday. "I expect we have to be more united in the near future to face the national challenge of building a better Indonesia."
That Susilo faces tough challenges is more than rhetoric.
The world's fourth most populous nation is resource-rich, but bedevilled by rampant corruption, unpredictable courts and weak economic growth.
"SBY has a very short time period to prove himself to be effective," said Jeffrey Winters, an expert on Indonesia at Chicago's Northwestern University, using Susilo's nickname.
"The message is if he[Susilo] doesn't produce on the rule of law, on corruption, on the economy, on jobs, on getting investment going, he's going to be thrown out too in five years"
"The message is if he doesn't produce on the rule of law, on corruption, on the economy, on jobs, on getting investment going, he's going to be thrown out too in five years."
Despite a popular mandate, Susilo must work with the incoming parliament, where Megawati's party and others have formed a coalition that comprises 55% of the seats.
A key player in the coalition, Golkar leader Akbar Tandjung, has already said his party - which has the most seats - and others in the group want to play the role of a balancing force rather than align themselves with Susilo.
Regional and local party leaders count on cabinet seats and the patronage that flows from them for their power.
Many Golkar officeholders have been growing restive over Tandjung's leadership. The party will be parliament's largest more by default than by any increase in its own popularity.
Its candidate came third in first-round presidential elections and it backed another loser in Megawati.
"This election is not only a rejection of Megawati, it also sends an earthquake through Golkar and PDI-P (Megawati's party)," said Winters.
"You can expect that those two parties are going to be in turmoil until they establish a new leadership and a new direction," he said, adding they would not be well-positioned to block Susilo in parliament.