Allardyce's four-year tenure came to a disappointing end when he saw his side slip from fourth at Christmas to 12th by the season finale at Newcastle United with just three wins in 2015.
The former Bolton Wanderers and Blackburn Rovers boss had always divided opinion at Upton Park.
But even the harshest Allardyce critic would concede the club has progressed steadily under his stewardship.
Co-owners David Sullivan and David Gold hired Big Sam to do a very specific job.
His skill set was what West Ham needed. He picked the club off the floor, rejuvenated the dressing room and got the team playing winning football again.
While the club most certainly ended up underachieving this season, overall things look in good shape at Upton Park, especially with the exciting move to the Olympic Stadium just a year away.
And now former Hammers defender turned manager Bilic has paid tribute to Allardyce for the situation he has inherited on his return to the East End.
"I know a lot about West Ham's current squad and the team is good, it has a good balance," Bilic told West Ham's official website.
“They were a little bit unlucky last year with the number of injuries in a crucial stage of the season, but the manager has done a good job and is leaving me a good team."
His first task in East London when he returns from a family holiday will be to improve that team further still.
West Ham's woes in the second half of last season can be directly traced to the glut of injuries Bilic has highlighted, which stretched Allardyce's resources.
Despite his admiration for the job done by Big Sam at the Boleyn, the lack of depth is a fact not lost on the former Besiktas and Croatia boss.
He added: "I definitely think the team can improve, as I said, last year they had some brilliant games, especially in the first half of the season. It will be my job to improve it and make it better."