Both the donor and the recipient are stable and recovering well, the official said.
Jaitley, 65, was admitted to the hospital on Saturday and taken to the operation theatre at 8 am today.
The minister, suffering from a kidney ailment, has been undergoing dialysis for the last one month.
"I am being treated for kidney related problems & certain infections that I have contracted," he had tweeted.
Jaitley did not elaborate but said he was "currently working from controlled environment at home".
"The future course of my treatment would be determined by the doctors treating me," he had said.
In September 2014, Jaitley underwent a bariatric surgery to treat weight gain because of a long-standing diabetic condition. The surgery was first performed at Max Hospital, but he had to be later shifted to AIIMS because of complications.
Jaitley had a heart surgery several years ago.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)