The 51-year old Simonovic is a renowned legal expert who previously was Croatia's ambassador to the U.N.
He will be the first holder of the post that was introduced in December.
Simonovic said Tuesday he would like to complete the judicial reforms necessary for Croatia's entry into the European Union before taking up the new post in New York.
Croatia, which declared independence from Yugoslavia in 1991, was often accused of human rights violations in the 1990s. Its record has improved since 2000, though the EU and human rights activists are still sometimes critical.