Dunn, 27, quit Rovers for Birmingham four years ago for £5.5m but a series of back and groin injuries ruined his spell at St Andrew's.
He returned last January in a £2.2m deal and is now fighting fit.
Dunn said: "I'd like to think this is my last move. I'm settled here and a bit of a home bird, I guess.
"I certainly don't see myself going anywhere else. I love this place and I hope I won't go anywhere else.
"I'm just desperate to prove to people I'm still a good player after all the injuries I've had."