Milanovic took the presidential oath before Constitutional Court President Miroslav Separovic, after the national anthem "Our Beautiful Homeland" was performed by singer Josipa Lisac accompanied by pianist Zvjezdan Ruzic, and a minute's silence was observed for the fallen in the 1991-1995 Homeland War.
He was sworn in for a term of five years and began his inaugural speech.
The first working day of the new president begins on Wednesday.
Presidential campaign director Orsat Miljenic will be the president's chief of staff, while the campaign's spokesman, Nikola Jelic, will be spokesman for the President's Office.