The FA says Hodgson was appointed on a four-year deal.
The FA overlooked the favourite, Tottenham manager Harry Redknapp, to hire a manager who has won eight league titles in two countries with three clubs and coached the national teams of Switzerland, Finland and the United Arab Emirates.
The 64-year-old Hodgson has had spells in club football in England, Sweden, Denmark, Norway, Switzerland and Italy, where he was twice in charge of Inter Milan.