Stormzy, 25, was speaking at his former school the Harris City Academy in Croydon, south London, where A-level students are opening their results.
The rapper told BBC Breakfast: "If you're academically brilliant don't think because you come from a certain community that studying at one of the highest education institutions in the world isn't possible."
The scholarship aims to encourage the admission of more black students to top universities, after none got into Cambridge University between 2012 and 2016.
Two successful Cambridge applicants this year and two next year will have their fees paid for by the scholarship.
Stormzy, real name Michael Ebenazer Kwadjo Omari Owuo Jr, revealed he harboured ambitions of studying at either Oxford or Cambridge when he was at school.
He said: "Luckily for myself when I was going through school, I had the academic ability.
"I was always reminded by my teachers that I was destined, if I wanted, to go down that road and study at one of the top universities.
"I diverted and ended up doing music so it didn't happen for me. I thought I was quite a rare case in that I knew that was possible.
"That's not always the case. When students are young, academically brilliant and getting great grades, they should know that's an option."
The Ivor Novello Award-winning artist offered words of encouragement to students across the country opening their results, admitting he did not get the grades he was hoping for.
Stormzy said: "As someone who used to class myself as an academic, I know how tough it is. I coasted through GCSEs, came to Harris Crystal Palace Sixth Form and started my A-levels.
"I remember coming to my results day and looking at my results and they shocked me. I didn't do too great at A-levels.
"That shock to the system showed me that education is a tough thing. When kids are dedicated and they're smashing it and getting great results, that's difficult."
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