The Frenchman joined Liverpool as a director of football strategy in November 2010, with his role redefined in March last year.
Later on Thursday it was announced that Dr Peter Brukner, the club's head of sports medicine and sports science, had also departed after spending two years at the club's Melwood training ground.
In a statement on Liverpool's official website, principal owner John Henry said: "We are grateful for all of Damien's efforts on behalf of Liverpool and wish him all the best for the future."
Chairman Tom Werner added: "The club needs to move forward and we now have a huge game on Saturday. It is important that everyone joins us in supporting the manager and gets behind Kenny and the team and focuses on a strong finish to the season."
Comolli presided over a big-spending recruitment policy which saw more than £100 million spent on the likes of Andy Carroll, Luis Suarez, Jordan Henderson, Stewart Downing and Charlie Adam.
Despite the vast sums spent on players, this season the Reds are in danger of finishing in the bottom half of the Premier League for the first time.
However, European football has already been secured for next season after Liverpool won the Carling Cup final in February, and they face local rivals Everton in an FA Cup semi-final clash on Saturday.
Comolli said: "I am grateful to have been given the opportunity to work at Liverpool and am happy to move on from the club and back to France for family reasons. I wish the club all the best for the future."
Comolli spent three years in a similar role at Tottenham Hotspur before he was sacked along with Juande Ramos and Gus Poyet in October 2008 with Spurs rooted to the bottom of the Premier League table.