The Northern Ireland Under-21 international made 38 appearances on loan at Alloa last season, scoring three goals.
The 21-year-old joined Celtic in February 2015 from Derry City, where he netted 13 goals.
Manager Paul Hartley said: "Michael impressed during his spell with Alloa and we look forward to welcoming him."
Dundee have added to their forward options by signing Celtic winger Michael Duffy on a season-long loan.