Murchie has put pen to paper on a one-year deal which will see him stay at Scotstoun until at least May 2017.
The 30-year-old joined the Warriors in 2009 from London Welsh and he has gone on to play 102 games for the club.
He made his Scotland debut in the 2013 quadrangular tournament in South Africa against the Springboks. Since then he has claimed two more caps.
Glasgow Warriors head coach Gregor Townsend said: “Peter has made a huge contribution to the club over the last seven years, so it’s great news that he’s staying with us.
“He sets the standard for the squad in how to conduct yourself as a professional and works very hard to improve as a rugby player.”
Heading out of Scotstoun is Bryce, will move to Edinburgh Rugby in the summer.
Bryce, 24, played 13 games for the club after graduating from the BT Sport Academy Stage 3 programme and has scored four tries.
Bryce told the Warriors website: “It was a really hard decision to leave Glasgow but I’m hoping to kick-on at Edinburgh and play as regularly as possible next season.”
Townsend added: “While it’s a disappointment that he won’t be with us next season, I’m sure that he will continue to progress and we wish him all the best at Edinburgh.”