オアハカ

In the team's search for a new venue, the owners of the Tecamachalco franchise received support from the Oaxacan state government. They also received support from a group of businessmen led by Carlos Ojeda of Laredo, who wanted to bring professional football back to the state of Oaxaca.

On December 10, 2012, the president of the Liga MX, Ascenso MX, and Decio de María made the official announcement at the state capital building of the start of a new football club. The name of the club was changed to "Alebrijes" following a vote by the public. The new name refers to the colorful folk sculptures made in the state.

On July 20, 2013, they played their first Ascenso MX game, drawing 2–2 with Atlético San Luis. On April 9, 2014, Alebrijes lost the Clausura 2014 Copa MX finals against Tigres UANL by 3–0 at the Estadio Universitario.

On December 2, 2017, Oaxaca defeated FC Juárez on penalties to win the Apertura 2017 Ascenso MX tournament.

On May 28, 2019, Oaxaca had an administrative change, and the franchise belonging to Grupo Tecamachalco was paused for a year so that its owners could find a new city and remodel the administration of the club. Meanwhile, the franchise belonging to Zacatepec Siglo XXI (on hiatus between 2017 and 2019) was transferred to Oaxaca to ensure the continuity of Alebrijes in Ascenso MX. In the first tournament with the new board, the team won the championship by defeating Atlético Zacatepec with an aggregate score of 5–3, with this, the team won the second league title in its history, also being the last trophy awarded in the history of Ascenso MX.