Szafnauer had long been expected to leave his role at Aston Martin, with Motorsport.com reporting back in November that he looked set to take up a senior role with the rival Alpine squad.
Szafnauer said he had "no intention" of leaving Aston Martin and that he had a long-term contract in place.
But Aston Martin announced on Wednesday that Szafnauer had left his role as team principal and CEO of its F1 squad.
"Otmar Szafnauer has left the company and his role at Aston Martin Cognizant Formula 1 team will be managed within the leadership team until a replacement is appointed," the statement reads.
"We would like to thank him for the service provided to the team over the past 12 years and wish him well for the future as he will undoubtedly take on new challenges.
"Fortunately, we are led and managed by a strong group of individuals, and we are comfortable to take a little time to explore options before announcing a new team structure.
"The focus of the team is currently on preparing the most competitive car possible for the start of the 2022 season."
Szafnauer first joined the Silverstone-based squad when it was known as Force India in 2009. He played a crucial role in navigating the financial struggles it faced in 2018 prior to its takeover by Lawrence Stroll, who ultimately rebranded the squad as Aston Martin for 2021.
In September, Aston Martin hired former McLaren F1 chief Martin Whitmarsh as its group CEO of its performance technologies arm. But Szafnauer said Whitmarsh's arrival did not impact his role with the team.
It emerged over the Brazilian Grand Prix weekend that Szafnauer could be set to join Alpine, but no news on his future plans have yet been announced.
Over the Interlagos weekend, Szafnauer said he was "as surprised as anybody else" to read reports that he could join Alpine, but fell short of denying he had been in contact with the team.