The Premier League newcomers have been in discussions with 28-year-old King for several weeks as they bid to strengthen their squad ahead of this weekend's season opener with Fulham.
King is manager Phil Brown's eighth new signing ahead of the Tigers' first Premier League season. Gardner had already been at the KC Stadium on a loan deal but the permanent deal makes him the club's record signing.
Brown said: 'I am more than pleased. We had a training session this morning and the missing link up front was there.
'Hopefully Marlon plugs that gap. Not being disrespectful to the players that we have, but he brings something different. He runs the channels, he gets behind, he is strong, he brings others into the play.
'I want players with points to prove and Marlon wants to prove he is a Premier League goalscorer.'
Brown is also hoping he can help resurrect Gardner's career after slipping down the pecking order at Spurs.
Brown said: 'Anthony did go there [Spurs] with high expectations.
'He got an England cap and things were running quite smoothly when he first arrived but then he hit a brick wall in terms of selection, injuries, form, pressure at the club.