Bono, the son of singer Cher and the late Sonny Bono, officially changed his gender from female to male in May last year, following the successful operations.
The LGBT activist has said that he plans to marry partner Jennifer Elia "within a year".
"We've been engaged actually for two years," Bono explained to host Piers Morgan on Tonight. "[We] kind of had to put things on hold a little bit."
Bono's mother Cher recently admitted that she had found it difficult to cope following his surgery, after realising that she would never hear her daughter's voice again.
Bono and Elia have been together for over six years, and are now able to legally marry following Bono's new-found legal status as a man.