The 26-year-old becomes Robins boss Gary Johnson's fourth new recruit of the close season, following Aaron Downes, Jack Munns and Kyle Storer.
Morgan-Smith started his career at Stockport County and has since turned out for Ilkeston Town, Luton Town, Macclesfield Town and Kidderminster Harriers. He won a cap at England C level during his time in the Conference.
Wolverhampton-born Morgan-Smith spent last season at League One Oldham, where he played under Johnson's son Lee.