The robot-assisted keyhole prostatectomy "went very smoothly", the Prime Minister's Office said in a statement.
Lee, who turned 63 on February 10, decided to go for a surgical treatment after an MRI on his prostate, performed in January, showed suspicious lesions and a subsequent biopsy found that one out of 38 samples contained cancer cells.
The operation was performed by Professor Christopher Cheng, the lead urologist at the Singapore General Hospital.
"The surgery went very smoothly, and he (Lee) is expected to recover fully," said Cheng.
This is the second time that Lee has suffered cancer. He was diagnosed with lymphoma in 1992, for which he underwent chemotherapy.
Cheng said that Lee's prostate cancer is not linked to his previous lymphoma.
The Prime Minister will be on medical leave for one week, during which Deputy Prime Minister Teo Chee Hean will be acting Prime Minister.