The boss told the club's website: "I'm delighted to have signed Eliot for the club. He's a very dangerous player who always looks like he can score goals with either foot.
"He's played and scored in Leagues One and Two and is a quick and bright, forward-thinking player.
"He's someone who we feel we can develop and will become capable of playing at a much higher level."
Richards scored five goals during his 11 games for Exeter.