Edwards, 23, has scored three goals in 127 games for the Shrimps since joining from Blackburn Rovers in May 2014, with two in 50 appearances last season.
The centre-half was named player of the year at Morecambe's awards night.
He is the third signing for the League One newcomers after the arrivals of Ruben Lameiras and Lionel Ainsworth.
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Plymouth Argyle have signed defender Ryan Edwards from Morecambe on undisclosed terms after agreeing a compensation package.