The attacker has featured for both the under-23s and under-18s, making 12 appearances and scoring six goals with the latter this season and started to train with the first-team last month.
Boss Roy Hodgson talked up the teenager on Friday and said: "We believe at Crystal Palace that he has a big future and that he will get better and better."
A day later he included Rak-Sakyi on the bench for the clash with Chelsea, a club where the 18-year-old spent time before he moved to Selhurst Park in 2019 after he failed to be offered a scholarship by the Blues.
Chairman Steve Parish told the official club website: "I'm delighted for Jesurun and his family and signing his first pro contract is something to be celebrated. His recent performances really have been impressive.
"Jesurun has already had the opportunity to train regularly with the first-team, even securing a spot on the bench in our Premier League squad, and I sincerely hope that today's news is one of many exciting milestones for Jesurun at Crystal Palace."
Rak-Sakyi, who is the fifth under-18 player at the club to sign professional terms this campaign, added: "It's a very big moment in my life.
"Something I have been working towards since I started playing football and I'm happy and grateful that I've come this far. I just want to keep pushing on."