The 33-year-old Aardsma is expected to be with the team for Tuesday night's game against San Diego. He will be making his first appearance in the majors since 2013, when he was 2-2 with a 4.31 ERA in 43 games with the Mets.
Aardsma was Seattle's closer in 2009-10, when he had a combined 69 saves. He is 15-17 with a 4.23 ERA overall with seven teams in eight seasons.
Aardsma will become the 17th pitcher used out of Atlanta's bullpen this season. The Braves used 15 all of last season.
Martin was previously optioned to Gwinnett on May 19 and recalled on June 1, is 2-3 with a 5.40 ERA.