Wales defender Matthews will be a Celt until May 2016, while Scotland winger Forrest's new contract keeps him at Parkhead until December, 2016.
Earlier on Friday, the Scottish champions confirmed that defender Mulgrew had extended his stay until the summer of 2016.
Matthews, 20, signed a four-year deal when he joined Celtic last summer after leaving Cardiff City. In January 2011, 21-year-old Forrest, a product of the Hoops' Youth Academy, penned a five-year contract.
The three new deals announced by Celtic ties in with manager Neil Lennon's promise to reward players for their performances.
Czech twins Filip and Patrick Twardzik signed new contracts last month while the Parkhead club are in talks with the representatives of Gary Hooper, Thomas Rogne and Victor Wanyama.