The 40-year-old is the latest high profile figure to leave the club this month after chairman Bruce Buck and director Marina Granovskaia.
Cech had held the role since retiring as a goalkeeper in the summer of 2019.
Chelsea are now under new ownership following sanctions imposed on former owner Roman Abramovich for his links to Russia president Vladimir Putin, who is leading an invasion of Ukraine.
US billionaire Todd Boehly completed a £4.25b purchase of Chelsea last month after Abramovich put the club up for sale.
“It has been a huge privilege to perform this role at Chelsea for the past three years," Cech told Chelsea's official website.
“With the club under new ownership, I feel now is the right time for me to step aside.
“I am pleased that the club is now in an excellent position with the new owners, and I am confident of its future success both on and off the pitch.”
Boehly, chairman and co-controlling owner, added: “Petr is an important member of the Chelsea family.
“We understand his decision to step away and thank him for his contributions as an advisor and his commitment to the club and to our community. We wish him the best.”
Cech spent 11 years of his playing career with Chelsea, helping the Blues win four Premier League titles, four FA Cups, the 2012 UEFA Champions League and the 2013 Europa League among other honours.
Cech holds the record for the goalkeeper with the most Premier League clean sheets (202).
