Dawson, who signed for Brig in 2021, has made 54 appearances across two seasons at the Sir Tom Finney Stadium.
He scored seven goals for Brig this season, as they made it all the way to the play-off final, but suffered late heartbreak at Warrington Town to miss out on promotion to the National League North.
His final goal came in a 2-1 victory over Lancaster City at home.
The 24-year-old has also featured for Morecambe and Lancaster City.
He joins a Macclesfield side keen to make their mark at step three, having been promoted as champions of the NPL West Division last season.
Picture Credit: Macclesfield
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