Reds boss Jurgen Klopp ends his search for reinforcements on the left side of defence, with the Scotland international due to arrive on Merseyside for his medical on Thursday.
Klopp was initially interested in signing Ryan Sessegnon, only to see the teenager commit his future to Fulham on a new three-year deal earlier in the off-season.
Robertson made 33 league appearances, 31 of those starts, for the Tigers last term as they suffered the dreaded drop. The 23-year-old also featured in the top flight for the East Yorkshire club during the 2014/15 campaign.
The Merseysiders will reportedly pay an initial £8 million for the defender, although the deal could rise up to £10m in add-ons.