The defender is set to become Chelsea’s third first-team arrival this summer.
The £21m fee will be split up with £14m being paid upfront and the rest divided between add-ons.
The full amount of the deal could be £21.7m, this depends on the clubs performances, and Rahman’s appearances.
£3.5m will be paid depending on Chelsea’s performance.
£700,000 when Rahman plays 20 games.
£3.5m when he reaches 100 games.
The Ghanian will become Filipe Luis’ replacement after he was allowed to return to Athletico Madrid after just one season at the Bridge.
It is thought the 21-year-old will undergo a medical this week.