The Saints are parting with £10.9 million to secure the 21-year-old, according to Sky Sports.
It is a direct payment of his buy-out clause, which explains the quick nature of the transfer.
Salisu has reportedly agreed a four-year contract with the Saints.
The player will quarantine for 14 days after his arrival in the UK, and then join up with his Saints teammates for pre-season training.
Salisu is an exciting young centre-back, and the Ghanian is someone manager Ralph Hasenhuttl has targeted since the January transfer window.