Allardyce will take charge of the team in the next 48 hours.
Allardyce has been out of work since resigning as Crystal Palace managerin May. "So I continue to do what I was asked to do five weeks ago". But the chance to turn around Everton's faltering ship has lured him back, and Allardyce is expected to have a watching brief at Goodison Park on Wednesday night.
"I've always thought Everton was a great club".
"Obviously, the club has gone through a hard spell", Allardyce said, "and hopefully I can put that behind us as quickly as possible and start looking upwards again".
Sky Sports also revealed that Everton also engaged in talks with highly rated Shakhtar Donetsk boss Paulo Fonseca.
Palace chairman Steve Parish agreed to his departure and it is believed the south London club would receive a compensation package of around £2m if Allardyce takes a new job before next summer.
Having spent heavy to bring in reinforcements over the summer, Everton have struggled to click this season; the Toffees now sit 17th in the Premier League, two points above the drop zone, and have already been dumped out of the Europa League, following a disastrous showing in the group stage.
Writing in his column for Paddy Power recently the soon to be Everton manager wrote about the sides troubles saying, "Everton are obviously in a bad place at the moment and, like every football club that is struggling, it's mainly down to a loss of belief".
His final game in charge was Wednesday's Premier League victory over West Ham at Goodison Park, which Allardyce watched from the stands. But, after taking four points from their first two games, Everton managed the same tally from their next seven fixtures and Koeman was sacked.