Robertson, 23, has gone from a supermarket job and part-time football with Queen’s Park to a Champions League side in the space of four years after joining the Reds in a deal worth around £8million.
He now has a chance to establish himself as the answer to a problem position at Anfield, which was filled for the majority of last season by converted midfielder James Milner.
And his route to the top has not been lost of Klopp, whose net outlay on the deal is negligible after midfielder Kevin Stewart moved in the opposite direction for a similar fee.
“For Andrew this is another big step on what has been a quite incredible personal journey in a very short space of time,” he told Liverpoolfc.com.
“I love his story; where he has come from professionally to reach this point. When you speak to him it is clear why he makes his progress. He has a burning love for playing football – he really loves the game.
“His attitude is outstanding – absolutely outstanding. His talent and skills – also very, very good.
“He has experience of this competition, the Premier League, and he has the mentality and quality to get even better. I know our environment will benefit him and help him push himself even more than he has already. This is a player who does not limit his ambition, I think.”
Robertson spent three seasons with the Tigers following his arrival from Dundee United, and joins the Reds on ‘a long-term contract’.
Robertson, who will wear the number 26 at Anfield, has won 15 caps for his country and scored his only international goal in a 3-1 friendly defeat by Roy Hodgson’s England in 2014.
He joins Mohamed Salah and Dominic Solanke as summer additions to Klopp’s squad.
Burnley made the early running for Robertson after Hull’s relegation from the Premier League but no deal was forthcoming, opening the door for Liverpool.
The 23-year-old told Liverpoolfc.com: “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.
“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.”
Announcing his departure, Hull said: “The 23-year-old full-back left the Tigers’ Portuguese training camp earlier this week to undergo a medical and finalise terms with the Merseyside club.
“Robertson arrived at the KCOM Stadium from Dundee United in July 2014 and went on to make 116 appearances for the club in all competitions, scoring five goals.
“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.”
The departure of former Tottenham midfielder Stewart was being worked on simultaneously.
Stewart made 20 appearances for Liverpool, including 11 in the Premier League, and has played for Crewe, Cheltenham, Burton and Swindon on loan.
Having flown to Portugal for his medical, Stewart could make his first Hull appearance in Saturday’s friendly against Benfica.
Stewart told www.hullcitytigers.com: “I’m delighted to sign for the club, I can’t wait to get started and get my boots on.
“It’s an exciting move for me and I’m looking forward to the challenge ahead.”