Mr Ivo Josipovic won 60.3% of the vote in the second round run-off, beating the mayor of Zagreb, Milan Bandic.
Correspondents say the result was expected, but the margin of victory even larger than polls had predicted.
Mr Josipovic has pledged to lead an "uncompromising fight against corruption" and to help the government complete EU membership talks this year.
The 52-year-old law professor and classical music composer succeeds Stipe Mesic, who will step down in February after 10 years as president.
”More just Croatia”
Addressing his supporters in Zagreb on Sunday evening after the official results were announced, Mr Josipovic said his victory was for "all honest people regardless of their voting preferences".
"This is a victory which we can all celebrate because it is my deep belief that all of us want a better and more just Croatia," he said.
"I deeply believe that all of us want to live in a country in which work is rewarded and crime punished, in a country of social security and justice."
His opponent, Mr Bandic, was tarnished by corruption allegations during the campaign.
The BBC Balkans correspondent, Mark Lowen, says that as president, Mr Josipovic will have very little say in policy making, but will hope to take the country into the EU by 2012, becoming the bloc’s 28th member.
He has been criticised for lacking charisma, but is likely to co-operate both with Brussels and the Croatian government, led by Jadranka Kosor, which has been urged to tackle corruption if its EU hopes are to be fulfilled, our correspondent says.
Croatians have been largely unenthused by this election, reflected by the low turnout of 50.3%, slightly up on the first round, he adds.
Frustrated with widespread corruption, they have also been hard hit by the global financial crisis, with Croatia’s economy likely to show barely any growth this year. Unemployment remains at around 16%.
Our correspondent says the new president will be hoping to restore popular faith in politics, as well as steer Croatia towards calmer and cleaner waters.
* Mr Josipovic, also visited and morally supported B.a.B.e. campaign in Zagreb, organized on ocassion of the International Day for the Elimination of Violence Against Women.
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