The 27-year-old agreed the move to the Tigers after being informed by Sunderland boss Paolo Di Canio he was no longer part of his plans.
Graham endured a miserable time on Wearside, failing to score in 13 competitive appearances since his high-profile £5million move from Swansea in January.
Graham told the Tigers' official website: "It's great to come to a club where everybody is on a high after winning promotion and I've only heard good things about this club.
"It's exactly the same as when I joined Swansea a couple of years ago, a club coming up into the Premier League. The stories for two clubs are very similar.
"I know I'm coming to a good club with a top manager, a fantastic stadium and some very good players."
Graham's move away from the Stadium of Light began to look increasingly likely last week when Tigers boss Steve Bruce indicated his interest in the player.
Graham flew home early from Sunderland's pre-season tour of Italy and after talks he set off to join his new team-mates in Portugal.
Graham scored 15 goals in 54 appearances for Swansea following the Welsh club's promotion to the top-flight in 2011.