The new Deputy Prime Minister is Robert Taipatau.
Brown and his cabinet took the Oath of Allegiance and were issued with their warrants during a formal ceremony at Government House conducted by the Queens Representative, Sir Tom Marsters.
He replaces Henry Puna who stood down to contest the Secretary General's role at the Pacific Islands Forum.
Brown, who has spent 10 years in parliament, was educated at Gisborne Boys High School, Massey University and the University of the South Pacific.
