The 19-year-old has signed a season-long loan deal with the Silkmen as he bids to get more regular football under his belt.
Burgess arrives at the Moss Rose after a successful season at Gigg Lane that saw him regularly feature for the Shakers.
He made fourteen starts for Bury last season, scoring 2 goals in what was his first season of regular action in the Football League.
Burgess made his Bury bow way back in the 2013/14 season as a 16-year-old and has had loans with Stalybridge Celtic and Norwegian side Bergsoy IL.