City Chasing Ashbee
Tigers boss Jan Molby said: "He's the competitive midfielder we've been looking for and he'll really strengthen our midfield.
"He's a decent size at over six feet and he has a very reassuring physical presence. He'll put his foot in and win tackles but at the same time he's got tremendous discipline and can also play.
"He's the type of passionate and committed player we're looking to sign. I know six or seven clubs are chasing him so that shows his pedigree."
Meanwhile Ashbee himself said: "I don't suppose there is any chance of United coming back in for me, which is a shame because I didn't want to leave.
"I'm based in the Barnet area at the moment, which is a consideration if I'm thinking about joining Hull. But they are a very ambitious club who have their sights set on the First Division."
Ashbee started his career as a trainee at Derby, but played just once before joining Cambridge in 1996. In 5½ years he has played over 200 games for United, scoring 11 league goals.