Former Alfa Romeo technical director and Ferrari engineering boss Philippe Krief, who joined Alpine in early March, has been appointed as Rossi's successor.
He will continue in his role as vice president of engineering and product performance until further notice and report to Renault Group CEO Luca de Meo.
Rossi "will now focus on special projects linked to the transformation of the Group".
De Meo said: "I would like to thank Laurent for his unwavering commitment over the last two years at the helm of Alpine.
"Laurent has set out a clear and ambitious strategy for the brand. He has put Alpine in the best possible position to achieve its long-term goals.
"Alpine is now ready to enter a new phase of its development and to become a brand of the future. take Alpine to new heights."
This change at the top arrives hot on the heels of Alpine restructuring its racing senior management set-up, with F1 engine chief Bruno Famin promoted to vice president of Alpine Motorsports.
He was to report directly to Rossi, with Szafnauer in turn going to Famin.
Rossi was appointed to the top job at sportscar firm Alpine in January 2021. His remit also covered the overall management of the F1 team.
He replaced Cyril Abiteboul, who was at the helm from 2014 as Renault poorly adapted to the 1.6-litre turbo hybrid rules and faced heavy criticism from engine customer Red Bull.
As the F1 team was rebranded from Renault to Alpine for 2021, Rossi outlined an ambitious 100-race plan to grow the team into a regular podium contender come the 2024 season.
While Esteban Ocon scored an unlikely victory in the 2021 Hungarian Grand Prix, the team has only logged one further top-three result since. Ocon finished third in the 2023 Monaco GP.
Last year, Alpine was praised for out-developing McLaren to finish fourth in the constructors' championship and set out to close the gap to Ferrari, Mercedes and Red Bull this season.
However, amid a poor start to the campaign - exacerbated by unreliability and penalties - Alpine has fallen to sixth behind McLaren and Aston Martin ahead of the Hungarian GP this weekend.
This difficult start to the term prompted Rossi to arrange an interview with French TV network Canal+ ahead of the Miami GP in May. He used the platform to blast his team as "amateurish".
Given the heightened scrutiny, many believed team principal Otmar Szafnauer to be under heightened pressure to keep his job.
This also followed Alpine's handling of the 2022 driver market when it lost two-time champion Fernando Alonso to Aston Martin and protege Oscar Piastri to McLaren.
Spyro