The 64-year-old will leave West Bromwich Albion after taking charge of the club's final two Premier League matches of the domestic season.
Hodgson will officially begin work in his fourth job in international football on Monday May 14, less than two weeks before England's friendly against Norway in Oslo and just four weeks before their opening Euro 2012 Group D fixture against France. His first game at Wembley will be another pre-tournament warm-up match on June 2.
Hodgson gave his first press conference as England manager at Wembley later on Tuesday.
West Brom chairman Jeremy Peace said in a statement: "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.
"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.
"Of course, with Euro 2012 around the corner, we appreciate that some of Roy's focus over the next 12 days will be on England matters.
"But we are delighted he will be seeing the season out with us.
"With the help of the coaching staff, he will prepare the team in his usual, meticulous manner as we finish what has already been a successful season."