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.
Mulgrew, who was also developed by the Scottish champions, has been one of Celtic's key players since Lennon brought him back to the club in 2010.
Speaking to the official Celtic website, the Scotland defender said: "It's good to get it signed and focus only on the football. Last year was a good one for me. I've been happy to be back. Things have been going well for me so hopefully that can continue.''
The former Aberdeen and Wolves player has become a favourite of the Celtic fans and he is looking to bring them continued success.
He said: "It humbles me to hear them singing my name and getting behind the team. Everyone appreciates it and it helps us. I know it's a cliche but they are the 12th man at times and it really helps the team."
Source: PA
Source: PA