Croatia's conservative opposition candidate was ahead in a runoff presidential vote January 11.
An exit poll put Kolinda Grabar-Kitarovic of the opposition HDZ party ahead with 51.4 percent of the vote, against 48.6 percent for incumbent Ivo Josipovic.
Josipovic, 57, who was seeking a second five-year term with the support of the increasingly unpopular ruling Social Democrats, won the first round of the election on December 28 by a narrow margin.
The presidency is largely ceremonial, but analysts say a win for Grabar-Kitarovic, who is 46, would bode well for the party's prospects in the more important general election due in late 2015. Grabar-Kitarovic is a former foreign minister and ambassador to Washington.
The president cannot veto laws but has a say in foreign policy and defense.
Croatia, which joined the European Union last July, has been in recession for six years.