Herdman replaces Patrick Kluivert after the Dutchman left by mutual consent following Indonesia's elimination from Asia's qualifiers for the World Cup in October.
The 50-year-old Englishman previously worked with New Zealand's women's team before leading the Canadian women's team to the bronze medal at the Olympic Games in 2012 and 2016.
Herdman then steered Canada's men's team to the World Cup in Qatar in 2022, the first time the country had appeared at the finals in 36 years. He most recently coached Toronto FC.
His first games in charge will be in March when Indonesia host the FIFA Series in Jakarta.