The Baggies are the eighth club Allardyce has managed in the English top flight but Sunday's 3-1 loss at Arsenal condemned them to the drop.
Allardyce's contract runs until the end of the 2021/22 season but he has yet to reveal his plans for next season and whether he will lead the promotion charge.
Both he and the club now have the option of a break clause.
Only Birmingham have suffered more top-flight relegations than West Brom's total of 11, while Allardyce has managed in 17 different seasons in the competition.
Allardyce, who was briefly in charge of England in 2016, has established a fearsome reputation as a relegation firefighter, rescuing a number of clubs including Sunderland and Crystal Palace.