The English Premier League club said Comolli had been promoted from his present post of director of football strategy after impressing owners John Henry and Tom Werner since his arrival at the club last November.
"In the short time that Damien has been at the club, he has impressed us greatly with his knowledge of the sport, his work ethic and his incisive intelligence," Henry said in a statement.
"He is a clear thinker and understands exactly what is needed to form a long-term, consistent approach with the philosophy we all share here."
Comolli had played a leading role in attracting strikers Luis Suarez and Andy Carroll to the club in January, Henry added.
Comolli has previously worked at Arsenal, Tottenham and St Etienne.
Meanwhile Liverpool named Ian Ayre as the club's new managing director. Ayre has been Liverpool's commercial director for four years.
Liverpool appoint Comolli
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