A shake-up of the F1 team three years ago, which at the time was undergoing its transition from Renault to Alpine, resulted in Brivio being appointed as racing director.
Brivio joined Alpine after leading Suzuki to the first MotoGP teams' title in its history, with Joan Mir securing the Japanese manufacturer its first riders' title since Kenny Roberts Jr in 2000.
After just over a year in his role with Alpine, the Italian was then moved out of the F1 team in 2022 to take up the role of director of racing expansion projects, notably overseeing the Academy.
It is anticipated Brivio will return to Moto GP in the new year as manager of Honda, taking over from Alberto Puig.
Reflecting on his time with Alpine, Brivio said: “It has been a proud chapter in my motorsport career to be involved in Formula 1 with Alpine.
“I would like to thank Alpine for the opportunity to experience Formula 1, which was my desire, and also for the chance to pass on some of my experience in motorsport to its young drivers in the Alpine Academy.
“I wish the team and the Academy the best in the future and I'm sure we will see many young drivers go on to achieve fantastic things in their careers.
“To play a small part in some of that success will certainly be something I will cherish.
“I am grateful to Alpine for accommodating my wish to pursue other opportunities which may – and I hope that they will – arise in the future.”
Expressing thanks for Brivio's “hard work and commitment over the last three seasons”, Alpine Motorsports vice-president Bruno Famin added: “His experience in motorsports has been extremely valuable, especially in the development and progression of the Alpine Academy.
“Davide's wish is to leave Alpine to pursue other opportunities and we have accepted his desire by mutually agreeing to part ways.
“We extend our best wishes to him in his next chapter of an already impressive career in motorsports.”
Alpine has confirmed that Julian Rouse will continue to oversee the Alpine Academy programme.