Jenkins, 34, has made a total of 154 appearances for Cardiff Blues and is currently in his second stint at the region after making his debut in September 2004 against Leinster.
Cardiff Blues have also confirmed that the region will be led by back row Josh Navidi, who this week signed a new long-term contract extension, during the World Cup period.
Confirming the news, Head Coach Wilson said: "Gethin has been an absolutely outstanding player for both Cardiff Blues and Wales over the last decade, is vastly experienced and has been playing some fantastic rugby in recent seasons.
"Gethin leads by example every time he pulls on the jersey and that was crucial characteristic that we were looking for when we looked at who would take on the captaincy.
"He is the consummate professional who demands the very highest standards from both himself and his team-mates, both on and off the field, and is an ideal role model for the younger players in our squad.
"Josh will lead the team throughout the Rugby World Cup and his commitment to Cardiff Blues has only been underlined by his decision to sign a new long-term deal and commit to our region.
"Josh also leads by example and I know the players will support him during the opening months of the new season."
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