Robertson underwent a medical at Melwood this week after being granted leave from Hull's training camp in Portugal and has put pen to paper on a long-term contract.
He will wear Liverpool's number 26 shirt this season.
"It feels a wee bit surreal just now. Obviously I'm delighted. There's been a lot of speculation over the last couple of weeks but I'm glad that the deal's finally been done and I'm a Liverpool player," Robertson told the Reds' official website.
"My family are proud of what I've achieved so far and they're all over the moon with the move, as well as me of course. We're all just looking forward to being part of the Liverpool family now.
"There's not many, if any, more special clubs than Liverpool. When you grow up as a kid you dream of playing with big clubs such as Liverpool and to make that a reality is a dream come true for me.
"I just want to prove to people that I can do it at this level, and hopefully I manage to do that this season and go on to do good things for this club."
A Hull statement read, "Everybody at the club would like to thank Andy for his efforts in a black and amber shirt, and wish him well for the future."