Campbell 44-year-old has left the Silkmen after eight months in charge of the Sky Bet League Two club.
He guided them to EFL security on the final day of last season, losing just two of their last 10 games, after being seven points off safety when he took charge in November.
Cambell said: “Macclesfield Town provided me with a great beginning in the managerial side of the game, as well as a fantastic learning curve which I am truly grateful for.
“I would like to thank all the players and staff for their support during my time at the Moss Rose and also all the loyal fans, whose belief at the end of last season ultimately played a tangible role in our success.”
A club statement added: “This has been conducted in the most amicable of ways and there has been total transparency between the club and Sol regarding the challenges which face lower league clubs such as Macclesfield Town.
“Sol’s passion, drive and football knowledge will always be remembered at the Moss Rose with fondness.”
Campbell’s last game in charge was a penalty shootout victory over Blackpool in the Carabao Cup on Tuesday night, after a win and a loss in their opening two League Two fixtures.
Danny Whitaker will take training on Thursday and Friday and is likely to take charge of the team at Northampton on Saturday.
Whitaker was caretaker manager following the departure of Mark Yates in 2018, until Campbell was appointed.