The two emerged practically neck and neck from the first round of polling two weeks ago, with Josipovic, a 57-year-old former law professor and classical music composer, just one percentage point ahead of Grabar-Kitarovic with 38.5 per cent of the vote.
The popular incumbent, the third president of the former Yugoslav republic since independence in 1991, is a member of the Social Democrats (SDP), the main force in the ruling coalition.
Turnout was 21.92 per cent at 0400 IST, four and a half hours after polling stations across the Balkan nation opened, the electoral commission said it was almost nine percentage points more than at the same time in the first round and for elections in 2010.
Although presidential powers are limited in Croatia, today's vote is seen as a key test for parliamentary elections later this year in which the HDZ is likely to make significant gains.
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Prime Minister Zoran Milanovic's government has become hugely unpopular after failing to revive Croatia's economy, which has been struggling with recession for the past six years.
"The recession ... Is not only the consequence of the global crisis in 2008. Problems are rather structural and the authorities have not been solving them," economic analyst Damir Novotny told AFP.
Hopes that entry into the European Union would be an economic boost for the small Adriatic nation of 4.2 million have faded.
Analysts say the ruling coalition has failed to reform the huge and inefficient public sector, improve the business climate and attract EU development funds.
While vying for a post that is chiefly ceremonial, the two rivals made campaign promises to overcome a grim economic situation.
Josipovic has vowed to initiate constitutional changes -- namely decentralisation -- as a way to revive the economy.