Gibaut was drafted by the Tampa Bay Rays in the 11th round of the 2015 Major League Baseball Draft.[6] He made his professional debut with the Princeton Rays and spent all of 2015 there, going 3-1 with a 2.12 ERA in 29+2⁄3 innings pitched in relief. In 2016, Gibaut pitched for the Bowling Green Hot Rods and Charlotte Stone Crabs where he compiled a combined 2-2 record, 2.53 ERA, and 1.25 WHIP in 57 total innings pitched, and in 2017 he pitched with Charlotte and the Montgomery Biscuits where he was 7-1 with a 2.21 ERA in 48 combined relief appearances between the two teams.[7] Gibaut spent 2018 with the Durham Bulls, going 4-3 with a 2.09 ERA and a 1.00 WHIP, striking out 75 batters in 56 relief innings pitched.[8]
The Rays added Gibaut to their 40-man roster after the 2018 season.[9][10] He began 2019 on the injured list with Durham.[11] After being activated, he pitched on a rehab assignment for Charlotte and then returned to Durham.[12]
On July 5, 2019, the Rays promoted Gibaut to the major leagues.[13][14] He made his major league debut on July 12 versus the Baltimore Orioles, allowing two runs and striking out two batters over two innings pitched.[15]
On July 28, 2019, Gibaut was traded to the Texas Rangers in exchange for cash considerations or a PTBNL.[17] He was assigned to the Nashville Sounds following the trade.[17] In 9 games for Texas in 2019, Gibaut went 1–1 with a 5.11 ERA over 12+1⁄3 innings. On December 2, 2019, Gibaut was non-tendered by Texas and became a free agent,[18] but was re-signed to a minor league contract with an invitation to spring training on December 19, 2019.[19] He appeared in 14 games for the Rangers in the 2020 season, collecting 14 strikeouts in 12+1⁄3 innings.
Minnesota Twins
On October 30, 2020, Gibaut was claimed off waivers by the Minnesota Twins. On February 19, 2021, Gibaut was outrighted off of the 40-man roster to make space for Matt Shoemaker and was invited to Spring Training as a non-roster invitee.[20] After appearing in 27 games for the St. Paul Saints, posting a 1-3 record with a 7.20 ERA and 46 strikeouts, Gibaut's contract was selected by the Twins on August 27.[21] Gibaut made 3 appearances for the Twins, recording a 2.70 ERA with 4 strikeouts. Gibaut was outrighted off of the 40-man roster on October 8.[22] On October 14, Gibaut elected free agency.[23]
Cleveland Guardians
On March 17, 2022, Gibaut signed a minor league contract with the Cleveland Guardians. The deal includes an invitation to the Guardians' 2022 major league spring training camp. On June 27, Gibaut was selected to the major league roster.[24] He was designated for assignment the following day after appearing in one game for Cleveland.[25]
Cincinnati Reds
On June 30, 2022, Gibaut was claimed off waivers by the Los Angeles Dodgers. He was designated for assignment on July 3 without appearing in a game for the organization.[26]
On July 5, 2022, Gibaut was claimed off waivers by the Cincinnati Reds.[27] In 33 appearances for the Reds, he recorded a 4.67 ERA with 48 strikeouts across 34+2⁄3 innings pitched.[28]
In 2023, Gibaut made 74 appearances out of the bullpen for Cincinnati, registering an 8–4 record and 3.33 ERA with 69 strikeouts and 3 saves across 75+2⁄3 innings.[29]
Gibaut was placed on the injured list to begin the 2024 season after suffering a strained forearm in spring training.[30] After experiencing "persistent issues" during his rehab, he was shut down from throwing[31] and transferred to the 60–day injured list on May 7, 2024.[32] On May 9, Gibaut underwent an anterior interosseous nerve release procedure to address the injury.[33] He was activated from the injured list on September 24.[34] In 2 games for Cincinnati, he allowed 1 run in 2 innings of work. On November 22, the Reds non–tendered Gibaut, making him a free agent.[35]