Grant, who spent a decade and a half as a midfielder and captain for Celtic, will move on at the end of the season - becoming the fourth confirmed managerial exit in central Scotland inside 24hours.
Falkirk dismissed co-managers Lee Miller and David McCracken on Wednesday and League Two Stenhousemuir saw boss Davie Irons leave with a 5-1 defeat at Annan Athletic marking his final day in post.
Grant spent two years at Alloa and finished eighth in 2019-20.
Chairman Mike Mulraney said:“The commitment and professionalism Peter has brought to Alloa has been a credit to him, we could not have asked for more.
“Obviously results this season have been disappointing, however it is with sadness we see Peter leave the club. I do however respect his decision and wish him the very best in his future endeavours.”