Souvik Pal, from Kolkata, had vanished after being separated from friends while celebrating New Year's Eve at a nightclub in Manchester city.
Souvik was found dead by specialist officers in Bridgewater Canal, near Manchester United's Old Trafford football ground, at 2pm (local time) yesterday.
Souvik had enrolled for product design course at Manchester Metropolitan University. He disappeared on a night out at the Warehouse Project in Trafford, Greater Manchester.
He was last seen at the event at about 11pm (local time) and was reported missing by a flatmate the following morning.
Souvik lived in Cavendish halls of residence on Cambridge Street.
A Greater Manchester Police spokesman said Souvik's family had been informed and officers were in regular contact with them.
Police which had pursued tracing Souvik offered condolences to the family and extended their support.
"Our thoughts and condolences are with Souvik's family at this devastating time and our officers are doing all they can to support them," said Detective Chief Inspector Colin Larkin.
"We do not believe there are any suspicious circumstances surrounding Souvik's death and a file will be submitted to the coroner in due course," he said.
A post mortem examination is due to take place later.
Souvik's father Santanu had travelled from his home in Bangalore to help with the search.
A number of appeals were made to trace his son, including the use of digital advertising hoardings at Manchester United's domestic Premier League of Football home game against Liverpool.
Souvik had trained for a part-time job serving refreshments at the stadium and worked at Manchester United's game against West Bromwich Albion on December 29.
Home Affairs Select Committee chairman Keith Vaz travelled to Manchester last week to meet Santanu Pal.
"I have spoken to Mr Pal and we are all aware of these developments, the last 22 days have been so difficult for him. I want to thank the police for their continued hard work on this case, everyone has done so much," the Labour MP said.
Santanu had earlier said his son was a "brilliant student" who had been awarded a Vice Chancellor's Scholarship by the university.
Souvik was offered places at universities in London and Singapore, but chose Manchester because of the "fantastic facilities".
"Everybody loved to have him as a friend and he was enjoying his life in Manchester. We have been told that by his friends. He had never been out India before and his friends in Manchester accepted him," Santanu added.