Graham made his mark playing for Swansea City after they were promoted to the top flight in 2011, scoring 12 league goals, but the arrival of Spaniard Michu the following year dropped him down the pecking order at the Welsh club.
The 27-year-old joined Sunderland in January, but failed to find the target for the north east club.
Graham said he had been told he was not part of Sunderland manager Paolo Di Canio's plans for the new season.
"I know I'm coming to a good club with a top manager, a fantastic stadium and some very good players," Graham said on the club website (www.hullcityafc.net).
Hull begin their Premier League campaign at Chelsea on August 18.
(Reporting by Toby Davis; editing by Alison Wildey)
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