The Scotland international signs a long-term deal on Merseyside after agreeing terms and completing a medical on Thursday.
The Reds will pay £8 million up-front with a further £2 million in add-ons for the defender, who will provide competition to converted left-back James Milner.
The 23-year-old is Liverpool's third signing of the summer after the capture of Dominic Solanke from Chelsea and the club-record £37 million signing of winger Mohamed Salah from AS Roma.
Reds new boy hails move as "a dream come true"
Robertson - who will wear the No.26 shirt for Liverpool - made 115 appearances for Hull, with 57 coming in the Premier League. He started 33 games last term, scoring one goal and assisting a further two.
Released by Celtic as a teenager, Robertson started out at Queen's Park before spending a season at Dundee United, where he left to join Hull in a £3 million move in 2014.
Robertson will meet up with his new team-mates next week upon their return from Hong Kong ahead of a trip to Germany for a clash with Hertha Berlin in Berlin and the Audi Cup in Munich.
Speaking to Liverpool's official club website, Robertson called his move "a wee bit surreal" and added that he was "delighted" that "the deal's finally been done."
Robertson - who worked in a supermarket and at Hampden Park just four years ago while playing semi-professional football with Queen's Park - added: "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."
The Scot declared that there's "not many, if any, more special clubs than Liverpool" and called it "a dream come true" to represent the club.
"I just want to prove to people that I can do it at this level," Robertson continued. "And hopefully I manage to do that this season and go on to do good things for this club."
Stewart moves to Hull in separate switch
Meanwhile Liverpool midfielder Kevin Stewart will move the other way in a deal worth £5.5 million rising to a potential £8 million, while Ryan Kent could join him in East Yorkshire in a season-long loan deal.
Stewart has officially completed his switch to the KCOM Stadium after leaving Liverpool's pre-season training camp in Hong Kong and while the two deals are separate from each other, they near enough represent a swap.
Stewart made 20 first-team appearances for Liverpool after arriving on a free transfer from Tottenham Hotspur but despite penning a new contract last November, was seen as surplus to requirements at Anfield and signs a three-year contract at Hull.
Hull - managed by former Russia boss Leonid Slutsky - are also keen on signing 20-year-old Liverpool winger Kent on a temporary basis, the youngster currently in Asia with the rest of Jürgen Klopp's first-team.
Robertson's arrival is also expected to pave the way for Alberto Moreno to depart the club. Liverpool rejected an offer from Napoli for the Spaniard last month as they hold out for a fee of £15 million.