Joe Aribo will undergo medical tests in the next few days in order to complete his move to Southampton, according to transfer market expert, Fabrizio Romano.
Aribo will link up with the Saints for a £6m fee plus add-ons which could rise to £10m.
The midfielder has also agreed personal terms with the Premier League club.
The Nigerian international is in the final year of his contract at Ibrox and has turned down offers of a new deal.
Southampton beat Nottingham Forest, Fulham and Crystal Palace to his signing.
Aribo scored 10 goals and recorded nine assists in 59 appearances across all competitions for Gers last season.