Wilson has penned a two-year extension, while Eddie has signed a new 12-month agreement. The news will come as a welcome boost to head coach Gregor Townsend ahead of Saturday's 1872 Cup second leg against Edinburgh.
Townsend has already secured fellow back-row men Rob Harley and Tyrone Holmes on fresh deals, and said: "Getting Ryan and James signed up adds further depth to the competitive group challenging for places in our back row next season.
"Ryan has improved every year since he's been at the club and is one of the most skilful back-row players in the game. He's very quick and has really good offload skills.
"He's put a lot of effort into improving physically and he tackles low and gets up and competes for the ball, which is what we like to see in our players.
"James is very popular and he's had an excellent season so far. He works very hard to improve himself and has made a big impact in a number of games this season. We always look to re-sign players we believe can drive us on to become a better side and Ryan and James will have big roles to play in our future."