Jaiba Brava

The club was founded on September 5, 1982 when the city of Tampico, Tamaulipas decided to buy out a struggling club made up from players from the Atletas Campesinos team from the city of Querétaro, Querétaro and some from the precursor club, C.D. Tampico A.C, that had been relegated and dissolved. That year the club struggled once again, finishing 14th in the league. The following year, the club would earn 9th place.

The 1985–86 season was split into two short tournaments (Prode 85 and Mexico 86). In the Prode 85 the club finished 1st in group 1 and qualified to the playoff series. In the quarterfinals the club defeated Cruz Azul 4–2. In semifinals the club defeated Puebla 5–4. In the finals the club went up against América, managing to beat América 4–1 in the first match and losing in the second 4-0 to a loss in aggregate of 5-1. In the Mexico 86 the club would once again reach the finals, this time after defeating Monarcas Morelia in quarterfinals and América in semifinals. The club would go up against Monterrey in the finals winning the first match 2–1 but once again losing the second match 2–0 and finishing runner up. The club would qualify to the playoffs again in the 1988–89 tournament. This time a short tournament play-off round was played with clubs Cruz Azul, Pumas de la UNAM and Atlante. The club would finish 1 point behind Cruz Azul, who would go on to final against América. The following year the club finished 19th overall. The club was bought out by the Querétaro franchise and moved to the city of Querétaro, Querétaro.

In 1991, Antonio Pélaez Pier bought the Atlético Potosino franchise and relocated it to Tampico, Tamaulipas to return the team to competitions. The team was registered in the Segunda División de México. In 1994, the team was promoted to the Primera División de México after defeating Irapuato in the championship final.

In the 1994–95 season the team played in the Primera División, however, in the middle of the season the club was moved to Querétaro and renamed TM Gallos Blancos, due to problems between the team owner and the oil workers' union, the stadium owners. At the end of the 1994–95 season TM Gallos Blancos was relegated to Primera División 'A', subsequently the owner moved the team to Hermosillo, Sonora and renamed it Gallos Blancos de Hermosillo.

After 1995, the team came and went on several occasions, playing mainly in the Primera División 'A' de México. Between 1995 and 1998 the team was a reserves team of Puebla. In 2001, Águilas de Tamaulipas was promoted from the Segunda División and took the name of Tampico Madero, however, the team only played one year until it was moved to La Piedad, Michoacán and renamed La Piedad due to a lack of support from local businessmen.

In 2005, the team returned to compete in the Primera División 'A', now as part of the sports structure of Atlante, Tampico Madero served as the team's reserves for a few years and later as an independent club. However, in 2009 it was dissolved due to the reform of the league that established requirements that the club had not met. The club was able to continue playing in the third level of Mexican football because it kept its reserves squad that took part in that league and became the main team.

In 2010, the team merged with Universidad del Fútbol, and became part of the sports structure of Pachuca, for which Tampico Madero received youth players from. In the Torneo Independencia 2010, the team was runner-up in the league after being defeated by Celaya. In 2014, the club became independent from Pachuca.

In 2015, the Grupo Tecamachalco took charge of the club with Javier San Román as president. In the Clausura 2016 tournament the team won the championship of its division and played in the playoff against Potros UAEM, where the club was defeated.

In the summer of 2016, Grupo Tecamachalco signed an agreement with Grupo Orlegi. With this agreement Tampico Madero obtained a franchise in the Liga de Ascenso de México, the second category of Mexican football, where the team was officially renamed as TM Fútbol Club. In 2018, Grupo Tecamachalco abandoned the operation of the club due to the possible elimination of the right of promotion for the clubs of the Ascenso MX to the Liga MX. After this event, Tampico Madero continued in the league, but became a training team for Santos Laguna and Atlas, the Orlegi clubs that participate in the Primera División de México.

In the spring of 2020, the Ascenso MX was in a financial crisis from the COVID-19 pandemic and the loss of television income and fans suffered by the clubs, so the league became a youth football development tournament and promotion to the Liga MX was abolished in exchange for member clubs receiving financial aid from teams in the highest category of Mexican football. The league was renamed as Liga de Expansión MX.

In December 2020, Tampico Madero became the first Liga de Expansión champion after defeating Atlante in the final. In May 2021, the team lost the champions trophy against Tepatitlán. In December 2021, the team was runner-up in the league after falling to Atlante in a repeat of the 2020 final.

At the end of 2021, several problems began to arise between Grupo Orlegi, the owner of the club, and the oil workers' union due to the worse state of the Estadio Tamaulipas, since both parties accused each other of not taking charge of the maintenance of the property. This terminated in the stadium being closed by the municipal government due to its poor conditions.

On April 20, 2022, Grupo Orlegi announced the end of the TM Fútbol Club franchise, which meant a new demise for the club. The next day the purchase of the franchise was announced by businessman Arturo Lomelí, the owner of Mazorqueros Fútbol Club, who decided to move the club to La Paz, Baja California Sur and rename it Club Atlético La Paz.