Edwards has been a key figure in Liverpool's successful recruitment programme, but the 42-year-old is ending his 10-year association as he wants a fresh challenge.
"I had always planned to cap my time at the club to a max of 10 years," Edwards wrote in an open letter.
"I've loved working here, but I am a big believer in change. I think it's good for the individual and, in a work setting, good for the employer, too.
"Over my time here we have changed so many things, hopefully for the better, but someone new brings a different perspective, new ideas and can hopefully build, or change, the things that have been put in place beforehand."
Edwards has been linked with a move to ambitious Newcastle following their Saudi-led takeover, although the Magpies' new manager Eddie Howe insisted on Wednesday he knew nothing about a potential approach from his club.
Liverpool manager Jurgen Klopp has benefited from Edwards' expertise, with players such as Mohamed Salah, Virgil van Dijk, Fabinho and Alisson Becker arriving to become the core of a team that has won Champions League and Premier League titles.
"I know he isn't leaving immediately or in haste, which is cool, so we still have some time to work together," Klopp said in a club statement.
"If we are as fortunate and blessed as we have been so far maybe we can create more special memories for our club in this remaining time."
Julian Ward, currently assistant sporting director, will be promoted after Edwards leaves, taking on the more senior role.