The 61-year-old Englishman -- who lost out to Steve McClaren 10 years ago after Sven-Goran Eriksson left -- signed a two-year contract with his task to guide England to the 2018 World Cup finals in Russia.
Allardyce -- who gained credit for keeping Sunderland in the Premier League last season -- replaces Roy Hodgson, who stepped down after England lost to minnows Iceland in the last 16 of Euro 2016 last month.
"I am extremely honoured to be appointed England manager especially as it is no secret that this is the role I have always wanted," said Allardyce in a statement issued by the FA.
"For me, it is absolutely the best job in English football.
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"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.
"I know we have talented, committed players and it is time for us to deliver."
The FA said Allardyce, who became favourite once Under-21 coach Gareth Southgate said he wasn't interested in the job and Arsene Wenger said he wanted to see out his contract at Arsenal, had been the unanimous choice of the three-man panel deployed to select the manager.
"Following a comprehensive and structured process, The Football Association is today delighted to confirm Sam Allardyce as England manager," read the statement.
The highly respected 61-year-old has signed an initial two-year contract and takes up the position with immediate effect following a successful spell retaining Sunderland's status in the Premier League.
"Allardyce's first match in charge will be a friendly fixture at Wembley Stadium on 1 September.
The FA said Allardyce, who was once accused by Jose Mourinho of getting his West Ham side to play '19th century football' though he retracted that comment a year later, has been set a number of tasks aside from reaching the finals in Russia.