The Scotland international became the Reds' third signing of the summer from Hull City on Friday, in a deal that could eventually rise to £10 million through additional instalments.
The 23-year-old, who penned a long-term deal with the club, played amateur football as recently as 2013 with Queen's Park - working in a supermarket to earn his keep.
From there Robertson joined Dundee United, where he made his Scotland debut and was crowned PFA Scotland Young Player of the Year.
He then joined Hull three years ago, making over 100 appearances for the Tigers and enjoying two seasons in the Premier League, though they suffered relegation on both occasions.
But Klopp saluted Robertson's impressive rise within just four years and hoped that Liverpool's new No.26 will be able to continue his rapid progression at Anfield.
Klopp backs Robertson to improve further
Speaking to Liverpool's official club website, the German insisted that the defender's move is "another big step on what has been a quite incredible personal journey in a very short space of time."
Klopp added: "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 revealed that Robertson "really loves the game" and enthused about his "absolutely outstanding" attitude while praising "his talent and skills" as "also very, very good."
Klopp noted that Robertson "has experience" of the Premier League but also "the mentality and quality to get even better", suggesting that Liverpool's "environment will benefit him" and "help him push himself even more than he has already."
Reds boss "really pleased" for extra depth
Robertson's arrival refreshes the Reds' options on the left side of defence, where natural midfielder James Milner covered for much of last season.
Alberto Moreno is expected to leave this summer while Jon Flanagan's future remains unclear, but Klopp named both of the pair when talking about his left-back options for the coming campaign.
He added that signing Robertson ensures Liverpool have "fantastic competition" in the position.
Klopp praised Milner for doing "very well" in an unfamiliar role last term and said he "can play most positions on the football pitch", continuing: "Alberto Moreno looks really good in pre-season and we have Jon Flanagan back, who can play left or right full-back. This signing strengthens us at full-back and I'm really pleased about this."