Wales's most-capped prop Jenkins, 27, was skipper for the Test clash with world champions South Africa back in November.
Jenkins said: "I'm happy at the Blues. Everything is being built off the field with the new stadium and training facilities and we've also made some good signings. Year after year we've been getting better and it's just a case of putting it all together to win trophies."
Sowden-Taylor has emerged from the shadow of Blues teammate Martyn Williams to stake his claim as Wales's first choice openside flanker after Williams's retirement after the 2007 Rugby World Cup.
Sowden-Taylor, 25, said: "We're moving forward as a region and I'm getting regular rugby. I'm really pushing myself everyday and it's great competition between me and Martyn."
Blues Coach David Young said: "It's pleasing that a player of Gethin's quality has signed a new contract and everyone knows it's inevitable that Robin will leap frog Martyn and be the number one not only here but also for Wales."