The 19-year-old was on the Number 5 First Bus service to Castlemilk, Glasgow, when the accident happened.
Police said he got on the bus at Stockwell Street at 12.25am yesterday before trying to leave the vehicle as it approached Victoria Bridge.
He then made his way to the rear of the vehicle as it was still moving. The 19-year-old then opened the emergency exit and jumped out.
As a result, he suffered serious head injuries and died at the scene. There were no other vehicles involved.
A Police Scotland spokeswoman said the man's death did not appear to be suspicious.
A spokesman said: "Around 12.25am on Sunday, a man got onto the bus at Stockwell Street, Glasgow.
"As it approached the Victoria Bridge, he tried to get off the bus but was unable to do so due to traffic in the area.
"He then made his way to the rear of the double decker bus, which was still moving, opened the emergency exit on the lower level and jumped out.
Victoria Bridge, which links Stockwell Street to Gorbals Street, was closed to traffic following the incident but reopened at around 6.35am yesterday.
A First Glasgow spokesman said: "We continue to assist the police with their inquiries, but at this stage our thoughts are very much with the victim's family and friends."