The 61-year-old signed an initial two-year deal after compensation was agreed with Sunderland, whom he steered to Premier League safety last season.
He succeeds Roy Hodgson, who quit after England were knocked out of Euro 2016 in the last 16 by Iceland.
Allardyce, whose first game in charge will be a friendly at Wembley on 1 September against as yet unnamed opponents, said he was “honoured”.
He added: “It is no secret that this is the role I have always wanted. For me, it is absolutely the best job in English football.
“I will do everything I can to help England do well and give our nation the success our fans deserve. Above all, we have to make the people and the whole country proud.”
Football Association chief executive Martin Glenn said: “His excellent managerial credentials, including his ability to realise the potential of players and teams, develop a strong team ethos and embrace modern methods that enhance performance, made him the outstanding choice.
“We could not help but be energised by his personal perspective on England’s future.Culled from the bbc.