The former Scotland No 2 was manager of Norwich City between 2006-07 and also had a spell as caretaker boss of Fulham.
Grant spent the bulk of his playing career with Celtic and earned two caps for his country. He also played for Norwich, Reading and Bournemouth.
Alloa are looking forward to another season in the Ladbrokes Championship and begin their Betfred Cup campaign at home to Elgin City on Tuesday July 16.