The goalkeeping great is the latest high profile figure to depart following Todd Boehly and Clearlake Capital's takeover.
He follows managing director Marina Granovskaia and chairman Bruce Buck in departing the west London side.
In confirming his exit, Cech said: "It has been a huge privilege to perform this role at Chelsea for the past three years. 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."
Co-owner Boehly 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."