[8][9] After he signed with the Mariners, he made his professional debut with the Everett AquaSox of the Low–A Northwest League for whom in 24+2⁄3 innings he had an ERA of 2.55.
On January 11, 2017, the Mariners traded Burrows and Luiz Gohara to the Atlanta Braves in exchange for Mallex Smith and Shae Simmons.
In 2019, he split time between Mississippi and the Triple–A International League Gwinnett Stripers, going 2–4 with a 4.42 ERA and 63 strikeouts over 57 innings.
[14] Burrows did not play in a game in 2020 due to the cancellation of the minor league season because of the COVID-19 pandemic.
Burrows began the 2021 season at spring training,[15] and returned to minor league camp in March.