The Reds have paid a mooted £20 million for the England cap from Sunderland.
Reds director of football Damien Comolli said: "I'm very pleased because he was one of the targets we had and when you get your first target it's always a good sign because you think the others will come through as well.
"We are very, very pleased. He has got all the skills technically that we needed. He's good with the ball, he's creative, he's got good passing, he's physically very good.
"That's everything we wanted in a midfielder and he's versatile as well. For Kenny he will be the player we wanted.
"On the fee, I've read and heard a lot of things. There was a lot of speculation on how much we would pay for Jordan and none of the figures I've seen are correct so far.
"We've paid a price that we are comfortable with, otherwise we would not have done the deal."