The team's roots lie with Campos Racing, the squad founded by former Formula One driver Adrián Campos in 1998. Campos Racing had competed in the GP2 Series since its inaugural 2005 season and won the teams' championship in 2008. After that title-winning season, Campos elected to step down and transfer control of the GP2 entry to Agag. Agag renamed the outfit after the addax antelope species and retained the name of team title sponsor Barwa International, a Qatari real estate company, creating the Barwa Addax identity for 2009.
Campos Racing itself continued to operate separately, competing in the European F3 Open Championship. In 2010 Campos launched a Formula One entry as Campos Meta 1 before being taken over and renamed Hispania Racing, making Addax and its predecessor indirectly linked to F1 through their common founder.
Addax made an immediate impact in the GP2 Series. For its debut 2009 season, the team signed reigning GP2 Asia Series champion Romain Grosjean alongside existing Campos driver Vitaly Petrov. Grosjean took the team's first pole position at Barcelona's opening qualifying session and followed it with the team's first race victory, leading Petrov home in a 1–2 finish. Both drivers quickly became championship contenders. Grosjean was called up mid-season to replace Nelson Piquet Jr. at Renault in Formula One, handing his seat to Davide Valsecchi. Despite missing the final eight races, Grosjean ended fourth in the standings; Petrov finished runner-up to Nico Hülkenberg. Addax took the 2009 teams' championship in its very first season under the new name.
For 2010, Petrov departed for Formula One with Renault and was replaced by Sergio Pérez, alongside returning driver Giedo van der Garde. Pérez rapidly became team leader, winning five races and mounting a sustained challenge to eventual champion Pastor Maldonado. Van der Garde contributed three podium finishes and seventh in the standings. Addax finished second in the teams' championship, just five points behind Rapax.
The 2011 season yielded the team's second teams' title. Van der Garde was retained and joined by Charles Pic. Although Van der Garde could not sustain early championship momentum against dominant leader Grosjean — now driving for DAMS — he reached fifth in the standings. Pic impressed more than anticipated, taking three pole positions and two race victories to finish fourth overall. The combination proved effective enough for Addax to win the teams' championship despite neither driver reaching the podium of the individual standings.
In 2012, with Pic and Van der Garde both moving on, Addax fielded the less-heralded pairing of Johnny Cecotto Jr. and Josef Král. Cecotto showed promise by winning feature races at Monaco and Hockenheim but was limited by inconsistency to ninth in the standings. Král's season was disrupted — he was replaced for several rounds by Dani Clos and subsequently by Jake Rosenzweig — but managed his own maiden series win at Monza before the season's end. Addax slipped to eighth in the teams' championship, and the team would not return for 2013.
Addax also took over Campos Racing's GP2 Asia Series entry. In the inaugural 2008–09 campaign, Petrov and Pérez scored three wins between them, with Addax finishing third in the teams' standings. For 2009–10, the team ran its main series line-up of Pérez and Van der Garde, supplemented by Max Chilton, Luiz Razia, and Rodolfo González at various rounds, finishing tenth in the championship. In the final 2011 Asia Series season, the team ran Van der Garde and Pic throughout; Van der Garde claimed two podium finishes and third overall, while Pic failed to score.
Addax was among the ten teams granted entries for the inaugural GP3 Series season in 2010, one of only two outfits — along with ART Grand Prix — also competing in GP2. In both its seasons in GP3 (2010 and 2011), Addax finished eighth in the teams' championship. The team withdrew from GP3 at the end of 2011.
In its four seasons of active GP2 competition, Addax established itself as a consistent front-runner, winning two teams' championships and serving as the proving ground for drivers who reached Formula One. Romain Grosjean, Vitaly Petrov, Sergio Pérez, Giedo van der Garde, and Charles Pic all made the step up to F1 after or during their time with the team. The operation represented the continuation of the Campos GP2 legacy under new ownership and is remembered as one of the sport's more consistently competitive outfits during the GP2 era.