The 26-year-old initially joined the Warriors from Boroughmuir on a three-month deal, and has impressed in his outings so far this campaign.
Born in Liverpool and a former Scotland U18 cap, Matthews made his competitive Glasgow debut in the opening match of the season away to the Toyota Cheetahs in Bloemfontein.
"I'm delighted to be staying with the Warriors," said the hooker.
"To be able to learn from established internationals and from coaches of the quality we have here at Scotstoun is a huge opportunity for me, and I've really enjoyed my time with the club so far.
"Hopefully I can continue to learn and push for selection over the course of the season."
Meanwhile, hooker Jack Iscaro has returned to parent club Old Glory DC following the conclusion of his time at Scotstoun.
Glasgow Warriors assistant coach John Dalziel said: "Johnny's come in and done a great job - he's continually driving towards improving himself as a full-time professional.
"He's made a great contribution to our environment and has a strong set-piece, and he's definitely a player that suits the style of rugby we want to play.
"We'd like to thank Jack - he's used every second of his time here to try and increase his skill set, and we look forward to following his progress over the course of the season."