According to the Liverpool Echo, the Reds have agreed a £10m ($13.1m) fee with the Tigers for the left-back. The Merseyside club will pay £8m ($10.4m) up front, while the remaining £2m ($2.6m) will be paid as add-ons.
With both clubs coming to an agreement over the transfer fee, it has now allowed the player to agree personal terms and complete his Liverpool medical. He will undergo his medical examination on 20 July, Thursday.
Robertson, 23, was part for Hull's warm weather training camp in Portugal.
The Scotland international departed the training camp in order to complete his impending move to Liverpool and is set to become the Reds' third signing of this summer.
Liverpool have already completed two signings so far in the ongoing transfer window. Dominic Solanke arrived on a free transfer from Chelsea, while Egyptian international Mohamed Salah was brought in from Serie A club Roma for a club-record fee of £36.9m ($46.9m).
Solanke scored his first goal for his new club in Liverpool's 2-0 victory over Crystal Palace in the Premier League Asia Trophy in Hong Kong. Salah also impressed for Jurgen Klopp's side against the Eagles.
Robertson will not join his new teammates in Asia for the pre-season tour. Instead, the left-back will travel to Germany and link up with the Reds for their friendly fixtures against Hertha BSC and Bayern Munich.
The former Borussia Dortmund manager will be hoping that Robertson can shine for Liverpool as he will be competing with James Milner for a place in the starting line-up. The ex-Manchester City man was deployed in the left-back position last season, ahead of Alberto Moreno.
Klopp is set to sanction the Spain international's sale following the arrival of Robertson.
Liverpool are hoping to raise around £15m ($19.5m) from the sale of Moreno, who arrived at the club from Sevilla in 2014.