The Scotland international will undergo a medical on Thursday to become the Reds' third signing of the summer having agreed personal terms.
The 23-year-old left Hull's pre-season tour of Portugal earlier this week after Liverpool's offer of £8 million up-front with £2 million in add-ons was accepted by the Championship side.
Robertson, who has just one year on his contract, has long been linked with Liverpool - who have moved for the defender after ending interest in Fulham teenager Ryan Sessegnon in May and receiving no encouragement from AS Monaco having enquired for Benjamin Mendy.
He made 39 appearances for the Tigers in the Premier League last season, scoring one goal and setting up three, though the Humberside outfit could not avoid top-flight relegation.
Robertson made 115 appearances for Hull since joining from Dundee United in a £3 million transfer in 2014. That followed a one-year spell in Queen's Park's first-team, having been released by Celtic as a teenager.
Several Premier League sides have shown an interest in Robertson, a natural left-footed left-back, but Liverpool have scouted him for the past two seasons and are close to wrapping up the deal. If all goes well, the Scot will be a Liverpool player by the end of the week.
Liverpool close in on Hull's Robertson with Stewart going the other way
With the Reds' first-team currently in Hong Kong for the Premier League Asia Trophy, Robertson will remain on Merseyside. He will train with his new team-mates for the first time in the club's training camp in Germany ahead of the Audi Cup next week.
His arrival will leave Liverpool with three senior left-back options for the time being, though Alberto Moreno is widely expected to leave this summer with the club hopeful of acquiring £15 million for the out-of-favour Spaniard.
Robertson will follow Dominic Solanke and club-record signing Mohamed Salah in joining Liverpool this summer and will provide competition for James Milner on the left side of defence.
The signing of Robertson will allow Liverpool more cover on the left with four competitions - should they navigate a Champions League qualifier - to compete in this term.
Left-back has long been a problem position for Liverpool, with Klopp looking to Milner to provide dependable relief last season, but the German will hope that Robertson can provide a long-term answer.
Hull are also closing in on a deal for Liverpool midfielder Kevin Stewart worth up to an eventual £8 million, while they are keen on a season-long loan deal for 20-year-old Reds winger Ryan Kent.
After a number of high-profile departures, including Harry Maguire, Curtis Davies, Tom Huddlestone and Eldin Jakupović, Hull boss Leonid Slutsky is looking to Stewart and Kent to boost their ranks.
The East Yorkshire side will pay £5.5 million rising to £8 million with add-ons for 23-year-old Stewart, who left Liverpool's squad in Hong Kong to discuss terms and undergo a medical.