Josh Lincoln, 19, was on the No 5 First service in Glasgow city centre going to his home in Castlemilk when the incident happened in Glasgow city centre.
Police said he got on the bus on Sunday at 12.25am in Stockwell Street but tried to leave the vehicle as it approached Victoria Bridge.
He then made his way to the back of the bus as it was still moving.
He opened the emergency exit and jumped out, suffering serious head injuries. The teenager died at the scene.
A First Glasgow spokesman said: "We can confirm that an incident took place involving one of our Service 5 buses at Victoria Bridge at around 12.25 on Sunday morning where a man exited one of our buses, whilst it was still moving, via the emergency exit. We continue to assist the police with their enquiries, but at this stage our thoughts are very much with his family and friends."
A Police Scotland 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.
"He then made his way to the rear of the bus, opened the emergency exit on the lower level and jumped out."
Officers are looking into the incident and a post-mortem examination will be held later.
There do not appear to be any suspicious circumstances surrounding the death.