The Olympic gold medallist attended Glasgow University's alumni Christmas dinner in Bute Hall to receive the reward in recognition of her achievements as Britain's most successful female rower.
Ms Grainger said: "It's incredible. I felt the big focus for me this year would be the Olympics, and winning it was everything I wanted it to be. I kind of thought I'd won everything I could win, so to be awarded this on top makes the year even more special."
Ms Grainger, 37, is the only woman to win a medal at four consecutive Olympic games.
She was born in Glasgow and returned to her home city in 2001 to study for a Masters in Medical Law and Medical Ethics after completing her undergraduate law degree in Edinburgh.
She is currently close to completing a PhD at King's College London.
Ms Grainger said: "I wouldn't have done a PhD if it hadn't been for the Masters at Glasgow. I used to really look forward to seeing the people in my class who I absolutely loved to work with. I remember them all being hugely supportive.
"When I can get outside it gets me awake and alert and then ready to go and do some thinking. So actually I do find that they're a good balance for each other."