Yeandle will miss the rest of this season after suffering a foot injury in the loss to Northampton last month which will need surgery.
But he will be able to have at least one more campaign at a club he has played for in every one of their major finals.
“It’s great to have the old warrior with us going forward,” director of rugby Rob Baxter said.
“The really pleasing thing, along with how well he’s been playing on the field, is how much leadership he brings to the group.
“It was a very easy decision to keep him as he truly understands what we’re about.
“He’s sorely missed right now through injury, but if there’s one thing I know about Jack it’s that he’ll turn up on day one of pre-season probably as the fittest player in the squad and prepared to work the hardest.
“While this injury is frustrating, it may actually extend his playing career because he can really focus on other elements of his physical conditioning. So, we’re really looking forward to working with him for another year.”
