Both players will be staying with the Warriors until at least May 2016.
James has made 119 appearances for the club during a 10-year spell in Glasgow, which has seen him become one of the longest-serving players at the club.
He skippered the Warriors Melrose 7s winning squad and has also represented Scotland 7s on the HSBC Sevens World Series.
James told glasgowwarriors.org: “I’ve spent my whole career in Glasgow and I’m very happy to have extended my stay at the club.
“The supporters are incredible and I love playing for the Warriors.”
Jerry joined the Warriors from London Irish in 2013 and the 30-year-old has gone on to make 30 appearances for the PRO12 side.
Jerry said: “My wife and I have really enjoyed the last two years in Glasgow and it was an easy decision to stay for another season.
“I’m looking forward to my third season with the Warriors and continuing to challenge for silverware.”
Glasgow Warriors head coach Gregor Townsend added: “It’s really good news for the club that James (Eddie) and Jerry (Yanuyanutawa) will be staying with us next season.
“Both players have played their part in getting us to the GUINNESS PRO12 Final and we’re lucky to have them.
“James has been with us for 10 seasons, while Jerry has been at the club for two years and both will continue to have important roles to play.”