Richards, 22, scored 12 goals in 69 games for City over the past three seasons, playing up front or out wide.
His signing follows that of midfielder Mitch Brundle from Gateshead on Sunday.
Another striker Jamie Allen was the first to sign earlier this month, moving from relegated Southport.
Richards began his career with home-town club Derby County, but was released in January 2013 and joined Ilkeston before signing for Chester in December 2014.
As well as their three new signings, Dover have also agreed a new deal with goalkeeper Mitch Walker.
Dover finished sixth in the National League, missing out on the play-offs by four points, while Chester slumped from seventh at Christmas to end in 19th, just avoiding relegation.
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Dover have made their third close-season signing by bringing striker Kane Richards to The Crabble on a one-year deal following his release by fellow National League side Chester.