A 6-2 defeat at MK Dons on Saturday proved to be Sheridan's last game in charge as the club's board, amid widespread reports of problems off the field, acted swiftly to end his reign.
Oldham are still handily placed in the League One shake-up, just one point behind sixth-placed Tranmere - who they play at home on Saturday.
Royle oversaw arguably the most successful spell in the club's history in the late eighties and early nineties, as he guided the Latics to the Premier League, two FA Cup semi-finals and a Littlewoods Cup final against Nottingham Forest in 1990.
His last game in charge of Oldham came in 1994, before he moved on to spells at Everton, Manchester City and Ipswich Town.
Royle is to be unveiled before the press on Monday afternoon.
Assistant boss Tommy Wright and coach Lee Duxbury are to stay with club.