The 28-year-old has penned a four-year deal at Ibrox until 2027 and moves to Glasgow for an undisclosed fee.
Browsing: Ibrox
The German-born Nigerian centre-back is out of contract at the end of the campaign.
The Daily Record claimed the St Mary’s side sent a representative to watch the 25-year-old during the Ibrox outfit’s 1-0 victory over Dundee United on Saturday.
Steven Gerrard’s side kept alive their ambitions of an unbeaten league campaign on Sunday as goals from Aribo and Ryan Kent proved enough to see off Hibernian at Ibrox.
Balogun did not take part in any of the Ibrox club’s pre-season friendlies after signing a one-year deal last week and was given a baptism of fire after being named in Gerrard’s starting XI for his side’s opening day trip to Pittodrie.
Manager Steven Gerrard has brought in the Nigerian cap on a two-year deal.
Liverpool winger Sheyi Ojo arrived on Monday morning at Rangers’ Hummel training centre ahead of a proposed season-long loan move.