The JV includes the Bafokeng Rasimone mine's North and South shaft, the Styldrift I and II projects, the BRPM concentrator complex and the Maseve concentrator plant.
Amplats said it was exiting the JV to focus on its own-managed mines and projects.
Royal Bafokeng already operates the mine.
Amplats said that it would keep its right to process 50% of the BRPM JV concentrate for the life of mine, while Royal Bafokeng will keep its termination right on the remaining 50% of concentrate every five years, with the earliest termination allowed in August 2022.
The transaction is subject to certain approvals and is expected to close in the September quarter.
Royal Bafokeng will pay part of the $135 million in cash, funded with a $14 million capital raise.
Capital contributions made by Royal Bafokeng to the JV before the completion date will go to paying down the balance, and the remaining outstanding consideration will be deferred as an outstanding loan at an interest rate equal to its borrowing rate plus a 2% premium.
Royal Bafokeng will then pay the deferred consideration in three equal tranches, with the first coming due after one and a half years from the completion date and the remaining two taking place each year thereafter.
Amplats' shares rose 1.83% Thursday to R367.96, while Royal Bafokeng's shares jumped 9.84% to R22 each.