The team was founded in 2004 under the name of Trans-Sil Târgu Mureș and in 2008 summer changed the name to FCM Târgu Mureș, becoming the city's main football team, as a successor to CS Târgu Mureș (dissolved in 1960), Mureșul Târgu Mureș (dissolved in 1964), and the original ASA Târgu Mureș (dissolved in 2005). They bought a spot from the newly promoted Unirea Sânnicolau Mare, consequently playing in the 2008–09 Liga II. FCM outperformed the predictions and played well throughout the season, winning 16 games and drawing 9, while scoring 54 goals and receiving 27, the fewest in the Seria II. At the end of the season, the team was very close to promote to the Liga I, finishing third with 57 points.
The following season, the club finished first in their series with 69 points, winning 20 games, drawing 9 and losing 3. The team scored 52 goals and received 20 (the fewest goals received in their series, like the year before) and was promoted for the very first time in its history to the Liga I. Eighteen years had passed since the city's last presence in the Romanian top football league (1991–92 season with ASA).
The next season, the club failed to maintain its position in the Liga I, finishing 15th, the highest place in the relegation zone. One team from the second division, Politehnica Timișoara, didn't receive its licence for the first league, so the Romanian Football Federation had to decide whether to keep the first team under the relegation line, FCM Târgu Mureș, or to promote the team placed third in the Seria II, behind Timișoara. Finally, the FRF decided that Gaz Metan Severin should be promoted, thus FCM ended up being relegated.
The board of directors fixed as an objective for the 2012–13 season the promotion back to the Liga I. However, the team couldn't keep the rhythm set by Corona Brașov and ACS Poli Timișoara, and after the first half of the season it was behind the earlier mentioned two in the league table. The second half of the season was even worse, FCM ending fifth in the West Division of Liga II, ten points behind ACS Poli, which took the second promoting place.
In 2013, the club changed its name from Fotbal Club Municipal Târgu Mureș to Asociația Sportivă Ardealul 2013 Târgu Mureș. At the end of 2013–14 Liga II they finished second and entered Liga I for the first time with the new name.
On 16 July 2014, the team debuted in Cupa Ligii (English: League Cup), Romania's secondary club football tournament, and lost their first ever match in the competition against CSMS Iași. It was an extraordinary season for The Red-Blues, securing their very first qualification in a European competition, by finishing second, and winning against two-time defending champions Steaua București both home and away. After the away victory over Steaua, Târgu Mureș seized the first place and was close to obtain a historical league title, however, after a 1–3 loss to Astra Giurgiu, the team fell back to the second place. However, Târgu Mureș kept chances to winning the championship after Steaua's 0–0 draw against CSMS Iași, having to win against relegated Oțelul Galați. Mureș side went to a 1–0 lead, but lost the title after Oțelul turned the score to 1–2.
On 9 July 2015, ASA earned its spot in the Romanian Super Cup as championship runners-up last season. The club faced Steaua in the final, which won the treble (Championship, Cup and League Cup), and defeated them 1–0, after a goal scored in the 63rd minute by Mircea Axente, who also received the "Man of the Match" title. The team was led by Dan Petrescu, who resigned after the match, due to the financial problems which had appeared in recent days. This was the club's first major trophy. Shortly after, it was revealed that Vasile Miriuță will become the new coach.