Wilson skippered Glasgow last season with Gibbins filling in when his fellow back row man was unavailable.
Wilson told glasgowwarriors.org: "I really enjoyed my first year as club captain last year and I'm chuffed to bits to not only be captain again but be co-captain with Cully.
"Since Cully arrived a year ago we've formed a good bond, we're good mates off the pitch and I'm sure we'll work well together."
Gibbins, who joined up last season from Hurricanes, said: "I'm really excited about it. I'm honoured to have been asked to work with Ryan and I'm really looking forward to getting ripped into the new season as a part of this squad."
Glasgow Warriors Head Coach Dave Rennie said: "We pretty much had co-captains last year. Obviously Ryan was our squad captain but he missed a number of games through injury and international commitments and Cully captained the side in his absence.
"They work really well together and we have a big squad of 50 players which is a lot to manage so they will share the role and the responsibility which will be good for both of them.
"They have complimentary skills, are both very passionate about this club and are hugely respected by all."