The polling stations will close at 7 pm.
None of the 13 candidates running for president in the first election round on January 2 won the majority of votes, and Mesic and Kosor entered the second round with the largest number of votes.
The head of the State Election Commission (DIP), Ivica Crnic, has called on voters to exercise their right to vote and go to the polls. Their vote is a contribution to democracy and an expression of the people's will, Crnic has said.
The candidate who wins more votes today will become Croatia's president.
First preliminary results will be announced at midnight by the DIP, the only body authorised to announce official election results.
At noon and 5 pm the DIP will inform the public about the turnout and possible objections and irregularities.
Around 4.4 million voters are eligible to vote - four million in Croatia and around 400,000 with residence abroad.
Out-of-country voting will take place from 7 am to 7 pm local time today in 50 countries at 155 polling stations. The first polling station that was opened in New Zealand last night, was closed when polling stations in Croatia were opened because of the time difference.
The run-off election is monitored by 2,039 monitors, 222 more than in the first round, of which 2,016 are domestic and 23 OSCE monitors.
Around 46,000 people are involved in the organisation of the elections and the second election round
will cost the government around 50 million kuna, as the first election round.
A two-day electioneering ban, which started in the first minutes of Saturday, will end at midnight today.