The Charlton ace, who is out of contract at this summer, will move north after being offered a lucrative offer by the Ibrox side.
According to the Daily Mail, Rangers will pay Aribo £20,000-a-week to see off competition fro the player.
The 22-yer-old has interested Celtic and a host of English club following his performances for the Addicks which saw him help the team into the Championship via the play-offs. He netted ten goals in 39 games.
The contract offered will see Aribo become one of the club's highest paid players on over £1million a year.
Last week, Charlton recruitment chief Steve Gallen warned the player from moving to Scotland for two reasons.
The club would lose out on money with Rangers only needing to pay around £240,000 for the cross-border development fee, while he also questioned how well the player would develop in Scotland.