Last month the departures of director of football Damien Comolli and head of sports medicine and sports science Peter Brukner were announced.
Owners FSG and the club issued a joint statement confirming the long-serving Cotton will leave on Sunday, the final game of the league season, by mutual consent.
"We would like to thank Ian for the important contribution he has made to the club during his long career here," managing director Ian Ayre told liverpoolfc.tv.
"He has played a key role as a member of the executive team in managing our relationships with key external stakeholders in the media and in the community. We wish Ian every success in his future career."
Cotton added: "It has been a privilege to be at Liverpool FC for the last 16 years.
"I would like to thank everyone I have worked with for all their support during that time and wish this great club all the best for the future."
The club say further information regarding the communications and community departments, which Cotton oversaw, will be announced in due course.
Liverpool have had a difficult time public relations-wise after their handling of the Luis Suarez-Patrice Evra racism row came in for widespread criticism earlier this season.
Players and manager Kenny Dalglish wearing T-shirts in support of the Uruguay international, who was subsequently banned for eight matches, was generally viewed as a particularly poor PR decision.