Agnew will link up with Hull manager Steve Bruce at the KC Stadium.
“I took a call from Steve Bruce earlier this week and he asked if he could talk to Steve. Aggers has an ambition to work at first-team level and I wouldn’t stand in his way,” said Middlesbrough boss Tony Mowbray.
“We’re disappointed because he’s a very good coach and he worked extremely hard with a young group last year. It will be a loss to us and yet we wish him well.
“He’s a good man and it’s a loss to us but a positive for Steve and I’m sure he’ll do well.”
