Burdi was added to the White Sox 40–man roster following the 2019 season.[10]
On August 8, 2020, Burdi was called up to the major leagues[11] and made his major league debut that night, pitching a scoreless inning against the Cleveland Indians. With the 2020 Chicago White Sox, Burdi appeared in 8 games, compiling a 0–1 record with 11.05 ERA and 11 strikeouts in 17+1⁄3 innings pitched.[12]
Burdi appeared in 6 games for the White Sox in 2021, posting an ERA of 6.00 with 6 strikeouts over 9 innings. On August 16, 2021, Burdi was designated for assignment by the White Sox.[13]
Baltimore Orioles
On August 18, 2021, Burdi was claimed off of waivers by the Baltimore Orioles. He was assigned to the Triple-A Norfolk Tides.[14] Burdi logged one scoreless appearance for Baltimore and posted a 2.25 ERA in 4 games for Norfolk to round out the year.
Washington Nationals
On October 15, 2021, Burdi was claimed off of waivers by the Arizona Diamondbacks.[15] He was released on March 14, 2022.
On April 21, 2022, Burdi signed a minor league deal with the Washington Nationals.[16] Burdi appeared in only eight games for the High-A Wilmington Blue Rocks, recording a 1.74 ERA with 10 strikeouts in 10.1 innings of work, making two scoreless appearances for the rookie-level Florida Complex League Nationals as well. He elected free agency on November 10, 2022.
Tampa Bay Rays
On January 18, 2023, Burdi signed a minor league contract with the Tampa Bay Rays organization.[17] He began the year with the Triple-A Durham Bulls, posting a 6.75 ERA with a 7:7 K:BB across 6 games. On April 26, Burdi had his contract selected to the active roster.[18] He made two scoreless appearances for the Rays before being designated for assignment on May 3.[19] He cleared waivers and was sent outright to Triple-A Durham on May 7.[20]
On May 17, Burdi was selected back to the major league roster after Yonny Chirinos was optioned to Triple-A.[21] After allowing 6 runs (5 earned) in an appearance against the Toronto Blue Jays, Burdi was again designated for assignment the following day on May 24.[22]
Los Angeles Dodgers
On May 26, 2023, Burdi was claimed off waivers by the Los Angeles Dodgers.[23] He was assigned to the Triple-A Oklahoma City Dodgers, where he made one appearance before he was designated for assignment on June 1.[24] He cleared waivers and was sent outright to Triple–A on June 6.[25] He pitched in three more games after being outrighted, with 4+2⁄3 scoreless innings overall.[9] He elected free agency on October 13.[26]
Personal life
His older brother, Nick Burdi, also plays professional baseball.[27]