Josipovic, a law expert and classical music composer who is relatively inexperienced in high politics, won 60.3% of the vote in the second round run-off, the state electoral commission said early on Monday.
He will be Croatia's third president since independence from Yugoslavia in 1991.
Populist Zagreb mayor Milan Bandic, backed by the Roman Catholic church and more conservative voters, took 39.7% of the vote as an independent candidate. He was expelled from the Social Democrats for insisting on running for president against the party's will.
On Friday, two days before the run-off, Croatia's anti-corruption police said it was investigating Bandic on several cases.
Josipovic promised to back Prime Minister Jadranka Kosor's drive to implement reforms and fight widespread corruption, as required by Brussels to complete EU accession talks this year.
"I want an uncompromising fight against corruption and organised crime. That is what I promised, that is what we'll achieve," Josipovic said, to the cheers of his supporters.
"I strongly believe that we all want a better Croatia with more justice, that we want a country where work is paid for and crime is punished," he said.
The candidate of the ruling conservative HDZ party failed to make it to the runoff. But Kosor, who took over in July and kick-started the new anti-corruption drive, remains the country's most popular politician.
"I believe Josipovic will support the government's efforts and that we'll cooperate well for the well-being of all our citizens," Kosor said on Monday.
New team for final EU drive
The HDZ last week expelled Kosor's predecessor, Ivo Sanader, after he announced a political comeback with a stinging attack on the party leadership and the government. Kosor later said she felt stronger than ever and determined to press on with reforms.
Zeljko Trkanjec, political analyst and editor at Jutarnji List daily, said Croatia had now got "a sort of a dream team," with Kosor and Josipovic in charge for the final stage of EU entry talks.
"They could function great together and that will help Croatia become a country with a real rule of law, which is the basic precondition for EU membership," Trkanjec said.
But Social Democrat chief Zoran Milanovic, boosted by his candidate's victory, quickly pointed to problems ahead, mainly in the struggling economy which contracted 6% last year.
"I am inviting the prime minister to meet and start discussing the serious problems, the unrealistic budget. We obviously want to continue spending more than we have, which cannot go on," he said.
Analysts say the government's biggest challenge is to salvage the strained budget, particularly as the government's macroeconomic forecasts of modest economic growth this year were seen as too optimistic.
Josipovic will succeed veteran reformer Stjepan Mesic, whose second five-year term ends in February. He will have limited powers over foreign policy, defence and the intelligence services but none over the economy or legislation.
(EurActiv with Reuters.)
