Downes, who joined the League One team in December 2018, was suspended for 28 days last month after an FA investigation found he had been placing bets on games.
FA rules, which tightened in 2014, ban anyone employed by a football club in England’s top eight divisions from gambling on matches.
According to the FA charges, Downes placed eight bets on football games in total from 2013 to 2019.
A club statement said: "Wally leaves on mutually agreed terms and with our sincerest gratitude for his time with the club, especially his invaluable contribution last season.
"While Wally’s FA disciplinary process concluded last week, the boards believe a change of first-team manager is the best option to help the club maintain its recent upturn in performances."
There have been a number of high-profile cases similar to this in English football this year.
Most notably, ex-England international Paul Scholes received an £8,000 fine this summer for placing bets while holding joint ownership of League Two side Salford City.
