Parry has failed to see eye-to-eye with manager Rafael Benitez over the club’s transfer policy.
Liverpool co-owner Tom Hicks told the club’s official website: “Rick’s commitment to Liverpool football club is epitomised by his desire to ensure that this transitional period is managed efficiently and we are grateful to him for his help. He will always remain a friend of the football club.”
Fellow co-owner George Gillett added: “I would like to thank Rick for his significant service to the club and the assistance he has given us since we joined Liverpool.
“He has been integral to the club’s success over the past decade and leaves with our best wishes for the future.”
Parry said: “I have had 12 very exciting years at Liverpool and am extremely proud of what has been achieved by the club over that period.
“The victory in Madrid was a wonderful reminder of the many high points we have experienced and adds to the moments that make Liverpool and its magnificent fans so special.
“It has been a privilege to serve the club and as a lifelong supporter I wish the owners, Rafa, the players and the wonderful staff all the very best for the future.
“I will be leaving at the end of the season knowing that the club remains strong and with a set of supporters who deserve success in all that Liverpool does.”
