The Reds will pay Hull around £8 million for the 23-year-old, who has a year left on his contract at the KC Stadium.
While Hull were relegated from the Premier League last season, Robertson was one of their most impressive performers, particularly following the appointment of Marco Silva.
Speaking to This is Anfield earlier in July, Hull supporter Joel Meloir of The Football Hipsters Podcast described Robertson as “technically good, quick and positive.”
“I feel Robertson can develop into a good full-back and at the reported £8 million price, this is a good piece of business for Liverpool,” Meloir explained.
“This is a step up for Robertson and he certainly has the attributes to be a success.”
Klopp is still interested in bringing RB Leipzig midfielder Naby Keita to Merseyside, too, and negotiations are likely to continue between the two clubs.