Omar Sadiq (32) was found seriously injured on Boydstone Road on the afternoon of Tuesday, 15 September, 2020.
He was taken to the Queen Elizabeth University Hospital where he died a short time later.
Uddin (28) entered his guilty plea when he appeared at the High Court in Edinburgh on Tuesday, 25 May, 2021.
He will return to be sentenced on Tuesday, 22 June.
Detective Chief Inspector Peter Sharp from Greater Glasgow CID said: “Our thoughts and condolences remain with Mr Sadiq’s family, who have been left devastated by his death.
“I hope today’s outcome will offer them some comfort, and allow them to move forward.
“Violence of this kind will not be tolerated in our communities, and Police Scotland will always ensure those who commit violent offences are brought to justice.”