Richards joins on a one-year contract and is Martin Allen's second signing of the summer following the capture of winger David Hutton from Tottenham.
The 28-year-old former West Brom trainee has had previous league stints with Bristol Rovers, Colchester and Peterborough.
Boss Allen told BBC Radio Gloucestershire: "Last season he got 21 goals and played 44 games, which is nearly a one in two strike rate.
"With Shane Duff agreeing to sign his contract it's two more pieces in the jigsaw.
"I wanted someone who wanted to come up and want to play for Cheltenham and somebody that I think has got something to prove to himself."