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.
Source: Autosport