The 21-year-old is currently leading the Formula 2 championship ahead of the final round of this weekend's F2 championship, where he holds a 14-point lead.
In a media release, Schumacher paid tribute to his parents for their support.
"The prospect of being on the Formula 1 grid next year makes me incredibly happy and I'm simply speechless," Schumacher said.
"I would like to thank Haas F1 Team, Scuderia Ferrari and the Ferrari Driver Academy for placing their trust in me. I also want to acknowledge and extend my love to my parents – I know that I owe them everything. I have always believed that I would realise my dream of Formula 1.
"A huge thank you must also go to all the great motorsport fans out there who have supported me throughout my career. I will give it my all, as I always do, and I look forward to going on this journey together with Haas F1 and them."
Although a seven-time champion, Michael Schumacher's life has been shrouded by mystery after he suffered a near-fatal brain injury in 2013 after falling and hitting his head on a rock while skiing in the French Alps.
He becomes the third Schumacher to race Formula One, with uncle Ralf Schumacher starting 180 races in a decade-long career.
Haas were pleased by the acquisition of the young star.
"I'm very pleased that we're able to confirm Mick Schumacher in our driver line-up for next season and I look forward to welcoming him into the team," Haas team principal Guenther Steiner said.
"The Formula 2 Championship has long served as a proving ground for talent to showcase their credentials and this year's field has undoubtedly been one of the most competitive in recent seasons. Mick has won races, collected podiums and excelled against some pretty exceptional talent in 2020.
"I firmly believe he's earned the opportunity to graduate into Formula 1 based on his performances. We have an opportunity ahead of us, as a team, to evaluate and nurture a new driver given our familiarity with our race package heading into 2021.
"We are putting in place our building blocks for the continued long-term growth of the team and I look forward to Mick's contributions both on and off the track in that process."
When Grosjean and Magnussen were moved on, F1's Lawrence Barretto said the strategy had changed for Haas with the team looking for "drivers with financial backing".
Schumacher, the most famous name in F1, and Mazepin, whose father Dimitry is a billionaire who owns a chemicals company, clearly fit the bill perfectly.
It comes after a horrific week when Grosjean was engulfed in a fireball at the Bahrain Grand Prix, after a first lap crash.
Luckily for the Frenchman, he suffered only burns to his hands and ankles and was released from hospital earlier today.
