He has previously played in MLB for the Chicago White Sox, Oakland Athletics, New York Yankees, Cincinnati Reds, and Milwaukee Brewers.

[17] The White Sox promoted Montas to the major leagues on July 17, 2015, to be their 26th man during that day's doubleheader.

[19] The White Sox promoted Montas again on September 1, and he made his major league debut as a relief pitcher the next day.

[20] On December 16, 2015, Montas, along with Micah Johnson and Trayce Thompson, were traded to the Los Angeles Dodgers as part of a three team trade that sent Todd Frazier to the White Sox and José Peraza, Brandon Dixon and Scott Schebler to the Cincinnati Reds.

[21] On February 12, 2016, the Dodgers announced that Montas underwent rib resection surgery and would miss up to four months of the season.

[24] On August 1, 2016, the Dodgers traded Montas, Jharel Cotton, and Grant Holmes to the Oakland Athletics in exchange for Josh Reddick and Rich Hill.

[25] After not getting a call to the majors in 2016, he appeared in 23 games for the A's in 2017, allowing 25 runs in 32 innings (7.03 ERA), while compiling a 1–1 record.

[29] On August 1, 2022, the Athletics traded Montas and Lou Trivino to the New York Yankees for JP Sears, Ken Waldichuk, Luis Medina, and Cooper Bowman.

[31] On February 15, it was announced that Montas would require arthroscopic surgery on his right shoulder and would miss the majority of the 2023 season.

[36] On July 30, 2024, the Reds traded Montas to the Milwaukee Brewers in exchange for Jakob Junis, Joey Wiemer, and cash considerations.

[38] On December 4, 2024, Montas signed a two-year, $34 million contract with the New York Mets including an opt-out after the 2025 season.