The 19-year-old was travelling on a bus shortly before 12.30am when the incident happened.
Police said he got on the bus at Stockwell Street 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 man then opened the emergency exit and jumped out.
As a result the 19-year-old suffered from serious head injuries and died at the scene.
It is understood he was travelling on a First Glasgow bus.
There were no other vehicles involved.
A Police Scotland spokeswoman said his death did not appear to be suspicious.
She added: "Inquiries are continuing.
"A post mortem will take place in due course."