Ambassador Peter Thomson beat out Cyprus's former deputy minister for European affairs, Andreas Mavroyiannis, by a vote of 94 to 90 in the 193-country assembly.
It was the first time a representative from the Pacific island states was chosen for the largely honorific post in the UN's 71-year history.
"It's a great moment for the Pacific islands," Thomson told the General Assembly.
"We bring special perspectives on climate change and on oceans issues," he said. "You can expect me to be vocal on these issues."
Thomson, who has been Fiji's UN ambassador since 2010, said he would also seek to build momentum for the UN's new development agenda, which lays out 17 global goals.
He succeeds Denmark's Mogens Lykketoft as assembly president.