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.
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.
Majority shareholder Farhad Moshiri and chairman Bill Kenwright reportedly had different ideas on who should take over the job on a permanent basis and pursuits of Watford's Marco Silva and Burnley boss Sean Dyche failed, while Ireland manager Martin O'Neill was also heavily-linked.
Watford’s Marco Silva was among the managers linked with the Everton job. Screengrab
A loss would see Everton sucked into the relegation zone.
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.
The sacking of Ronald Koeman in October has not produced the desired effect, with Everton recording one win, one draw and five defeats in all competitions since Unsworth took over.
Allardyce has been out of management since his surprise decision to quit Crystal Palace at the end of last season, having succeeded in a six-month mission to keep them in the top-flight.
He previously held talks with the club's hierarchy only to announce he had withdrawn because he felt they were hesitating.More news: Ole Miss names interim Matt Luke its permanent coach