O'Dea, 24, is looking forward to linking up with Simon Grayson's side and wants to help the Whites secure promotion back to the Premier League.
"I'm delighted to be here," O'Dea told the club's official website. "I'd been looking to get away and as soon as I heard of Leeds' interest I had no doubts.
"I played in the Championship with Ipswich last season and it's a very competitive division. Teams at the bottom can beat teams at the top and it's a test I'm really looking forward to.
"I'm hoping to achieve what everyone here is hoping to achieve - promotion. 20 teams will be aiming for that, but the players here did well last season and I hope I can bring a bit more to that."
The Republic of Ireland international is now hoping he will be involved in Leeds' opening game of the new Championship season at Southampton on Saturday.
He added: "Hopefully it'll be straight into it. I didn't see Southampton last season, but they will come up with a winning mentality and it will be a tough game.
"It's a nice stadium, there'll be a good atmosphere, and we're looking to do well."