Barmby said: "It had to be something special for me to leave Liverpool because I enjoyed it there.
"I heard of Leeds' interest and the chance to work with Terry again, that was the only move for me.
"He is the biggest influence on my career, at Spurs and England. You learn a hell of a lot from Terry.
"It's a thrill for me and I'm looking forward to it.
"The players here are up there with those of any other team and, with the managers direction, we can do well this year."