The midfielder joined the Tigers one year ago for a fee of £3m from Stoke City. Previous to that Stoke signed him from Wolves also for a fee of £3m.
His most successful spell was at Wolves where he started 123 League games scoring 16 goals.
He made 11 starts and 8 subs appearances in the Premier League for Hull last season.
He has completed his move today and will watch the Bluebirds face Burton tomorrow before being in contrention for a place in the team against Derby on Saturday.
Could be an excellent signing. A powerful midfielder, he joins Jason Koumas, Tom Heaton and Danny Drinkwater as new additions this summer.