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."
Premier League club West Brom confirmed on their website that Hodgson, who replaced now Chelsea caretaker coach Roberto Di Matteo last year, would remain in charge for the final two games of the season before joining up with England on May 14.
"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 is a vastly experienced coach who has won eight league titles since starting his coaching career with Swedish side Halmstad. He has also coached national sides, including taking Switzerland to the 1994 World Cup finals and Euro 96.
His club career has included stints at Inter Milan, Blackburn Rovers, FC Copenhagen and Fulham, who he took to the Europa League final in 2010.
However, his biggest club job in England ended in disappointment when he left Liverpool by mutual consent in January, 2011 after just 31 games in charge.
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.
