Hull boss Phil Brown told BBC Radio Humberside: "The deal between ourselves and Middlesbrough has been agreed.
"It's now just a matter of fine-tuning the deal between us and George and that's a process that does take time," he added.
Boateng said in March that he would remain at Middlesbrough as long as he remained a first-team regular.
His agent Barry Silkman told BBC Sport: "He has a year left on his contract, but he's been there for five or six years and given them good service.
"He played about 80% of the season, but he just thinks that maybe it is the right time to move on.
"Middlesbrough recognise he has been a great professional and say they won't hold out for a king's ransom should he wish to leave and won't stand in his way."