David Unsworth will remain in charge of the Blues for tonight's Premier League match against West Ham United at Goodison Park.
With Unsworth overseeing his final match at home to West Ham tonight, Allardyce's first game in charge will be against Huddersfield Town at Goodison Park this Saturday.
Former England boss Allardyce ruled himself out of the running earlier this month, claiming he did not feel the Toffees were convinced he was the right man.
Allardyce said: "I've always thought Everton was a great club".
Allardyce returns to club management six months after resigning from Crystal Palace, having saved the London side from relegation.
"Fatigue may be a factor because it's such a short period of recovery time and looking at the load these players have had over the last few months... every month has been like Christmas because of the number of games", Allardyce said.
Oumar Niasse and Michael Keane are available for selection against the Terriers
Everton's successful Under-23 coach David Unsworth has been in temporary charge since Koeman's departure and had some support to be appointed full-time but has won just won and lost five of his seven games at the helm.
Everton are now two points above the relegation zone going into Wednesday night's match against West Ham.
That victory, when the Toffees came from two down late on to secure a 3-2 victory over Watford, looked like it might be a turning point.
Everton, now 17th in the table, have won just one of the seven games under Unsworth, losing five, and fan opinion turned sharply with their last two outings - a 5-1 home loss to Atalanta and a 4-1 reverse at Southampton.
The club's prospects had appeared so different at the beginning of the season with Everton having invested heavily following last season's impressive seventh-place finish.
Everton's chief problem is clear to see.
Everton were 16th in the Premier League this morning and just two points above safety on the back of a dismal start to the season.
Former Obama Photographer Trolls Trump's Time Magazine Obsession
For comparison's sake, at this point in his presidency, Obama had played 26 rounds of golf, according to CBS News' Mark Knoller . A law enforcement source said Trump played with golf legend Jack Nicklaus, a longtime supporter of the President.