Hodgson left the position after failing to qualify Finland for the Euro 2008 finals and he subsequently took over as manager of English Premier league side Fulham.
The 54-year-old Baxter was in charge of the South African national side from 2004-2005 and has been coach at several Swedish clubs including Helsingborg since 2006.
Finland, who have never before qualified for the World Cup finals, have been drawn in a tough group that includes Germany, Russia, Wales, Azerbaijan and Liechtenstein.