Despaigne and fellow Cuban defector Aledmys Díaz held a showcase for Major League Baseball teams on 13 February 2014.[4] Despaigne signed a minor league deal with the San Diego Padres on 2 May 2014.[5] The Padres assigned Despaigne to the San Antonio Missions of the Double-A Texas League, where in two games started, he allowed one earned run in 7+2⁄3innings pitched. The Padres promoted Despaigne to the El Paso Chihuahuas of the Triple-A Pacific Coast League on 26 May.[6] Despaigne was called up by the Padres on 23 June to start that night against the San Francisco Giants.[7]
Despaigne pitched seven shutout innings, allowing four hits in his major league debut.[8] In his fifth major league start on 20 July, Despaigne pitched 7 2/3 no-hit innings before the New York Mets' Daniel Murphy doubled. The Padres won the game 2–1.[9]
The Miami Marlins claimed Despaigne off waivers on 15 September 2016.[12][13] He started a game for Miami against the New York Mets on 6 May 2017, allowing eight runs (three earned) in an 11–3 loss, and on 17 May returned as a relief pitcher, giving up two runs and four walks in one inning pitched. He was sent back to the Triple-A New Orleans Baby Cakes and was recalled on 28 July 2017.[14]
Los Angeles Angels
On 14 August 2018, the Marlins traded Despaigne to the Los Angeles Angels for cash considerations.[15] He made his first start with the Angels on 17 August against the Texas Rangers. He elected free agency on 5 November 2018.
Cincinnati Reds
On 7 January 2019, Despaigne signed a minor league deal with the Cincinnati Reds. He opted out of his contract on 16 May.[16]
Chicago White Sox
On 19 May 2019, Despaigne signed a minor league deal with the Chicago White Sox.[17] He made his first start with the team on 10 June against the Washington Nationals.[18] He finished 0–2 in 3 starts for the team. He elected free agency following the 2019 season.
KT Wiz
On 10 November 2019, Despaigne signed a one-year, $900,000 deal with the KT Wiz of the KBO League.[19] On 16 December 2020, Despaigne re-signed with the Wiz for the 2021 season on a one-year, $800K contract.[20] He posted a 13–10 record with a team-leading 3.39 ERA and 165 strikeouts over 33 starts. On 30 December 2021, Despaigne re-signed with the Wiz for the 2022 season on a one-year contract worth up to $1.35 million.[21] He became a free agent after the 2022 season.
Mariachis de Guadalajara
On 24 February 2023, Despaigne signed with the Mariachis de Guadalajara of the Mexican League for the 2023 season.[22] In 18 starts for Guadalajara, he compiled a 5–6 record and 5.22 ERA with 81 strikeouts across 98+1⁄3 innings pitched.
Leones de Yucatán
On 1 December 2023, Despaigne's rights were traded to the Leones de Yucatán in exchange for Anthony García.[23] He made 18 starts for Yucatán in 2024, posting a 3–7 record and 4.74 ERA with 78 strikeouts across 98+2⁄3 innings pitched.