Prithwish Mukherjee and Soham Dan, both from the department of computer science and engineering, had the highest CGPA score of 9.75.
Each year, the President of India Gold Medal is given to the student with the highest academic performance.
"It was a tie. We have some rules for a tie-breaker also but we thought that since both of them had worked equally hard both should get the award. It was a special gesture from the board of governors," instituter's director P P Chakrabarti said.
The medal was given yesterday, on the first day of the two-day convocation of the IIT.