Ethan Matthews, from Burry Port, Carmarthenshire, was told in December 2014 he needed the non-functioning organ removed.
He was put on an urgent waiting list at Cardiff's University Hospital of Wales without success until his parents were given the date of 17 May on Tuesday.
Ethan's father Robert Matthews said the family were "over the moon".
Mr Matthews said the family missed a phone call on Monday and when they rang back on Tuesday, they were told they could have the operation.
Ethan will have tests at his GP surgery beforehand, with the information sent to the hospital so any potential infections can be treated ahead of his surgery.
Mr Matthews said: "We're over the moon. Ethan was really pleased, really happy with it. We can't wait for it - we've had such a stressful time over the last two-and-a-half years.
"We can't wait to have it done so Ethan can get on with his life and be a normal teenager.
"Your teenage years are some of the best of your life, he's missing out on so much. He'll lead a perfectly normal life with one kidney, he just needs the one removed."
Ethan's operation was originally due to take place in January, but had to be cancelled because he had a urine infection.
Before Ethan was given his date for surgery, Cardiff and Vale University Health Board said the time a patient waited was based on factors such as clinical urgency and the type and complexity of the surgery required.
Ethan is fitted with a tract in his side after suffering from a build up of fluid and visits his GP up to three times a week to have his dressing changed.
At the moment, he is unable to play contact sports or go swimming with his friends.
"If he gets bumped playing football, it causes him a lot of pain and with swimming there's a risk of infection," said his father.
Ethan's family will take him into hospital on 16 May for last-minute checks before his kidney is removed the following day.
A 14-year-old who has waited two-and-a-half years to have a kidney removed has been given a date for his operation.