Barmby made just 17 league starts during two years at Leeds.
He blames Reid and Gray for refusing to pick him during his last 16 months at Elland Road.
"There's nobody been more disappointed than myself with what happened at Leeds," said Barmby. "You can train Monday to Friday all you want, but you need that carrot on a Saturday. I didn't have that at Leeds and I missed it.
"I really want to enjoy my football again and to come to Hull and play is a massive opportunity."