Clyne, 24, will return from holiday to complete the formalities of a deal which will be worth an initial ??12.5million with additional payments, based on certain conditions, to add up to a total of ??15million.
Clyne moved to St Mary’s from Crystal Palace in 2012 and made 41 appearances for Ronald Koeman???s team last season, earning his first England cap in November.
He played the full 90 minutes in a 3-1 European qualifying victory over Slovenia this month, and has gone on to make four international appearances.
Liverpool have been swift in their transfer dealings so far in the current window, landing striker Danny Ings, midfielder James Milner and goalkeeper Adam Bogdan??on free transfers as well as young Brazilian attacker Roberto Firmino from Hoffenheim for ??21.3million and defender Joe Gomez, for ??3.5million, from Charlton.