Explaining why he set up the scholarship, Stormzy tells Radio 1 Newsbeat: "In school and college I had the ability and was almost destined to go to one of the top universities.
"But that didn't happen for myself... so hopefully there's another young black student out there that can have that opportunity through my scholarship."
He adds: "I always said that there's a whole bunch of academically brilliant, excellent students who also need an incentive."
Cambridge has been criticised for not admitting many pupils from a black, Asian and minority ethnic (BAME) background.
In June, the university asked for help from schools and parents to increase the number of black British students it enrols.
It was after the Financial Times found that some Cambridge colleges didn't take in any black students from 2012 to 2016.
The university says that it admitted 58 black students on to undergraduate courses in 2017.
"We're going to have young black students who are academically brilliant and smashing it, and they should just have that opportunity to walk into a university like Cambridge," says Stormzy.
The 25-year-old announced the scheme at his old school Harris City Academy in south London on A-level results day.
He didn't go to university, but did get six A*s, three As and three Bs at GCSE.
"It sounds corny coming from a rapper, but I did love learning and I loved studying so I enjoyed that side of things," he says.
"But also, I made some of the best friends of my life at school, and so many memories."
Julia, who goes to Stormzy's old school, got three A*s in English literature, history and government and politics.
As a result, she's on her way to Cambridge in September.
"I didn't really know that someone that famous and that influential could come from my school," she says.
"I'm definitely going to apply for the scholarship because it seems like something that students who struggle with their financial situation at university may really benefit from, especially if they come form background similar to mine."
She thinks that black students are less likely to apply for universities like Cambridge because "they see it like a really distant, alien place that they would not really thrive in".
"But in reality, if you have the ambition and have the grades, there's no reason why someone from a similar background to mine can't apply there and be successful."