Hull and Liverpool have agreed a fee for the 23-year-old midfielder, which could reach £7.5m with add-ons.
Stewart will fly back from Liverpool's pre-season tour of Asia to discuss terms with the championship club.
The boyhood liverpool fan did sign a long-term contract in November, but since then has only made three appearances for the Liverpool first team.
With Jordan Henderson and Emre Can ahead of him in the defensive-midfield pecking order, Jurgen Klopp's side have allowed Stewart to move to pastures new in search of first team football.