Formula 2 runner-up Hadjar takes the place of New Zealander Liam Lawson, confirmed on Thursday as teammate to four-time world champion Max Verstappen at the main Red Bull team.
"The journey from karting through the ranks in single-seaters, to now being in Formula 1 is the moment I've been working towards my whole life, it is the dream," Hadjar said in a statement.
"I feel like I'm stepping into a whole new universe, driving a much faster car and racing with the best drivers in the world. It'll be a huge learning curve but I'm ready to work hard and do the best I can for the team."
Lawson, 22, has replaced Mexican Sergio Perez, whose dramatic collapse in form this season led to him being dropped despite having a contract for next year.
Hadjar will be the third French driver on the 20-car starting grid next season, along with Alpine's Pierre Gasly and Haas's Esteban Ocon.
The 20-year-old is also the fourth driver to graduate from a particularly strong 2024 Formula 2 championship, the others being champion Gabriel Bortoleto (Sauber), Kimi Antonelli (Mercedes) and Oliver Bearman (Haas). Lawson finished third in F2 in 2022.
"His journey to Formula 1 has been nothing short of outstanding, he has shown remarkable growth, with a series of impressive results in the junior single-seater ranks," team principal Laurent Mekies said of Hadjar.
"He has the talent and drive necessary to compete at the highest level and we have every confidence that he will adapt quickly and make a significant impact. I believe Isack and Yuki will make a great team."
Hadjar's appointment by the Italy-based team had been expected even before Lawson's promotion was confirmed.
"Isack is another talent, he's quick. He jumped in the car, he was faster than Yuki in the test last week which turned heads," team boss Christian Horner had told reporters before the announcement.
"He's definitely a raw talent, he needs a little bit of polishing but he has the speed.
"He was unfortunate in Formula 2 to miss out in the last race due to technical glitches with his startline software but he's impressed as well. It will be interesting to see how things pan out."