The 64-year-old, who has been in charge of Premier League West Bromwich Albion since February last year, became the 13th permanent post-War England manager after succeeding Italian Fabio Capello.
"The Football Association is delighted to announce the appointment of Roy Hodgson as England manager," the FA said in a statement after a second day of talks at its Wembley headquarters.
"Joining from West Bromwich Albion, Hodgson has agreed a four-year deal to become the full-time manager of the Three Lions."
"Roy's appointment as England Manager is obviously disappointing news for the club as we would have liked him to sign a new contract, which was in the process of negotiation, and remain as our head coach," West Brom chairman Jeremy Peace said in a statement.
"But we understand Roy's desire to take the England job and he will leave us after the Arsenal game on May 13 with our best wishes. We are delighted he will be seeing the season out with us."
Hodgson's first task will be to select a squad for the European Championship and prepare a side for the June 2 friendly against Belgium at Wembley.
Stuart Pearce was put in temporary charge of the team after Capello resigned in February and Tottenham Hotspur's Harry Redknapp was widely thought to be the overwhelming favourite to get the permanent job.
