A salary close to the £6 million per season that Koeman earned is understood to have been agreed as the 63-year-old prepares to take the reins at Goodison Park.
Allardyce will take charge of the team in the next 48 hours.
The pair worked under the veteran Premier League manager during his most recent spell in management with Crystal Palace which ended in May.
Allardyce was due to attend the club's USM Finch Farm training complex this afternoon in order to complete the formalities of a deal that is reported to be worth £9m over 18 months.
"The attraction of the club itself, the people I've known at the club - Peter Reid is one of my best mates, so are Andy Gray and Paul Bracewell whom I worked with at Sunderland - these people have always made me aware of just how special and unique a club Everton is and I feel really enthused and energised to come in as manager", Allardyce said.
Everton are now sitting 17th in the table, two points ahead of the Hammers.
Everton have lost seven of their 14 league games this season and can not qualify for the knockout stages of the Europa League after earning one point from their five Group E matches.
Allardyce re-emerged as the leading contender for the job this week after Everton were forced to accept defeat in their attempts to persuade Watford to part with Marco Silva.
It's five weeks since the Toffees dismissed Dutchman Ronald Koeman thanks to a poor run of form that saw them slump to third from bottom in the Premier League. So with that in mind it's no wonder Everton are throwing a lot of money at a manager who's never been relegated.
Former England boss Sam Allardyce is being strongly linked with the vacancy and talks are said to be taking place between the club and his representatives.
His first game will be at home to Huddersfield on Saturday, and he will no doubt want to cap his first game off with a victory. But that turned sour after only one match, with Allardyce stepping down in September 2016 following a newspaper sting.