The Scottish international has signed a three-year contract with Hull and moves for an undisclosed fee.
Marshall spent eight years at Cardiff and played 275 matches for the Bluebirds.
He joins fellow Scotland internationals Allan McGregor, Andy Robertson, Robert Snodgrass and Shaun Maloney at the KC Stadium.
Hull are also said to be close to the signings of Tottenham's Ryan Mason and Manchester United's young striker Will Keane.