Jensen was an ever-present during the 2009/10 season, which ended in the club being relegated from the remier League.
Manager Brian Laws said: "We are delighted Brian has agreed to sign the two-year deal we offered. He is a quality goalkeeper and someone who has served this club with distinction.
"He is not only a great servant, but a great ambassador and, even at his age, we feel Brian has good years ahead of him. We hope to drive him on further this summer because clearly we would like to strengthen in that area.
"It is something we are trying our hardest to achieve so that Brian has real strong competition, which can only improve his performances for the club."
Jensen, who arrived from West Brom in 2003, has now followed Stephen Thompson and Michael Duff in signing new deals.