The 48-year-old victim suffered serious facial injuries in the assault in Waddell Street in Gorbals.
The attackers, who are described as white males aged in their 20s, approached the man from behind and attack-ed him with a bladed weapon.
The incident happened at around 11pm on Tuesday.
Following the attack the two men ran off towards Glasgow Green.
The victim made his way to the city's Victoria Infirmary for treatment.
Police have appealed for witnesses who may have been in the area of Waddell Street or Ballater Street at the time of the attack.
They are reviewing CCTV images in hunt for clues.
Detective Constable Sandy Ward of Gorbals CID urged anyone with information to contact the police.
He said: "This was a nasty attack on a man who was making his way home from a night out.
"Due to the severity of his injuries, he has been scarred for life.
"We are continuing extensive inquiries into the incident, and we are accessing all CCTV that is available to us.
"I'd like to appeal to anyone who was in the vicinity of Waddell Street, Ballater Street at the time of the incident to get in touch with police on 101.
"Alternatively please contact Crimestoppers on 0800 555 111 where information can be passed in confidence."
Last month the Evening Times reported how the number of knife attacks in Glasgow has fallen by more than half in five years.
Figures obtained under our long-standing Crime on Your Street investigation showed there were 903 knife assaults in the city in 2012-13, down 57% from 2006-2007. They showed the number of knife attacks was down more than a third compared to the previous year.