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The 28-year-old forward has won 95 caps since making his debut against Australia in February 2003, scoring 40 goals, and was named captain of United two weeks ago.
He succeeds Liverpool midfielder Gerrard, who stepped down after England's group-phase exit at the World Cup, and will begin his tenure as permanent captain in next week's friendly at home to Norway.
"I think Wayne's an obvious choice and he certainly deserves it," Hodgson told journalists.
"His commitment to the cause, his experience, the fact he's already captained England in the past, and now he has the responsibility at Manchester United - all these factors weighed on my thought process."