Windass, 39, had grown frustrated at a lack of first-team opportunities with the Tigers and has opted to move to Boundary Park, with an option for next season in place if he impresses.
Windass told the Hull Daily Mail: "It is sad to walk away from Hull, but I've given it as long as I could and it's clear I'm not going to play for them in the Premier League.
"I've no problem with that, or with [manager] Phil Brown. If it wasn't for him, I wouldn't have had a second chance to play for the club I love and the opportunity to score a Wembley promotion goal.
"I haven't fallen out with Phil and I never would. We've had nothing to fall out about. He hasn't picked me, he's the manager and all I've wanted to do is play. He knows he's right and I know I'm right."