The boy, who was 14 at the time, was approached by Savile whilst waiting for an X-ray in 1994.
The new victims identified themselves following the publication of a report on Savile's activities at the infirmary was published in June.
It said 60 people were abused by him at the hospital over a 50 year period.
Leeds Teaching Hospitals NHS Trust investigation team were provided with a further eight names, six victims and two witnesses, following the publication of the initial report.
The teenage boy, known as KM, was one of them.
He told investigators he had been taken to the X-ray department on his own and was left sitting in a wheelchair wearing a dressing gown, when he was approached by Savile.
"He came and lent over me and told me to cheer up and said, 'Things can't be that bad'," he said.
"He put his hand on my leg, as he said it and then all of a sudden just moved his hand under my gown because I had a hospital gown on, I just had me dressing gown draped over me, put his hand on my genitals and squeezed them.
"It wasn't a long time and then looked at me and said, 'Now then I bet that's cheered you up'."
He said he had come forward in order to make it clear Savile had also abused male victims.
Another male victim, 29,  also reported being groped whilst waiting for an X-ray, in 1988.
The new accounts also include a student nurse who said she was assaulted in a linen closet, in the early 1980s.
One witness also said she had been warned about a "pink-haired man" by a ward sister as she was sent to the hospital's mortuary in 1954.
She was convinced the man was Savile, though no evidence of his association with the LGI as far back as the 1950s has been established, and was angry senior staff seemed to know about him.
Reports into Savile's activities at The Yorkshire Ambulance Service, Calderdale and Huddersfield NHS Foundation Trust, Leeds and York Partnership NHS Foundation Trust all found no evidence of abuse.
The Department for Education has also published a report by Leeds City Council into allegations of abuse at children's homes and schools.
However, the investigation found no evidence to corroborate any of the allegations.
A teenage boy who was groped by Jimmy Savile at Leeds General Infirmary, is one of six new victims who have come forward to investigators.