Russian business student Anton Dementyev, 19, was with three friends when Andrew Wilson's articulated lorry hit them on Argyle Street.
Andrew Wilson, 55, from Ripon, North Yorkshire, pleaded guilty to causing Mr Dementyev's death by careless driving on 8 May 2013.
He will be sentenced next month.
Wilson also admitted causing severe injury and permanent disfigurement to the other occupants of the car - taxi driver William Tombe and students Juan Doval, from Madrid, Camillo Herrara, from Columbia, and Daulet Abalov, from Kazakhstan.
Glasgow Sheriff Court heard that Wilson had gone through a red light on Argyle Street, at the junction with the M8, and collided with the Skoda taxi at about 23:20.
The lorry, which had been travelling at 34mph in a 30mph zone, pushed the taxi into a Kingston Bridge support pillar.
Mr Dementyev had been on his way to a nightclub to celebrate the end of his university exams.
Following the crash he was taken to hospital with a severe head and neck injury but died the following day.
The court heard that Mr Dementyev was in the middle seat in the back of the taxi. None of those in the back were wearing seatbelts, but a pathologist later confirmed that a seatbelt would not have saved Mr Dementyev.
When police arrived at the scene, Wilson told them: "I didn't see the second set of lights."
Defence counsel Simon Gilbride said Wilson has been driving since he was 17 and had held an HGV licence for more than 30 years.
He said his client wanted to give his condolences to all those involved, particularly Mr Dementyev's family.
Sheriff Kenneth Mitchell said: "This is a particularly sad and tragic accident because the accused failed to observe and obey a red traffic light causing the collision in which one young man sustained injuries which he would not survive."
He added: "The accused has been a driver for many years and has held an HGV licence for more than 30 years. He has no previous convictions and this is also a tragedy for him."
A lorry driver has admitted causing the death of a student after he drove through a red light and crashed into a taxi in Glasgow.