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The team was founded in 1994, after the old CB Canarias club, that huge financial problems at that time, merged with other teams of the Spanish island of Tenerife, to create the new Tenerife Canarias club, which only played two seasons in the Liga EBA competition, at the time when that league was the second tier level of Spanish club basketball.

People who were in disagreement with that merger then created the new CB 1939 Canarias club, which inherited the colors and the logo of the club. In 2012, Iberostar Canarias was promoted to Spain's top-tier level Liga ACB competition, after the team won the championship of the LEB Oro. However, the club couldn't actually promote, due to the club's inability to fulfill the requirements needed to join the league that are requested by the league's organizer, the ACB. One month later, on 20 July 2012, CB 1939 Canarias finally achieved the league promotion, after Lucentum Alicante's vacated place in the league was granted to CB 1939 Canarias.

Alejandro Martínez, became the team's head coach in 2003, and he managed to lead the team to multiple league promotions, going up from the LEB Plata (Spanish third tier), to the top-tier level Liga ACB. He resigned from the team's head coaching position in 2015.

Golden era and international championships

In the 2016–17 season, Canarias returned to the European scene after 28 years. On 29 March 2017, Canarias qualified for the 2017 Final Four of FIBA's Basketball Champions League (BCL), which happened 36 years after the club's first league promotion up to Spain's previous top level competition, the Liga Nacional, in 1981. The 2017 Champions League Final Four was played at Canaria's home arena, the Pabellón Insular Santiago Martín. Canarias won the BCL championship, after beating the Turkish Super League club Banvit in the Final. The championship marked the first major title in the club's history.

On 24 September 2017, Canarias participated in the 2017 FIBA Intercontinental Cup, as the defending champions of the Basketball Champions League. The club won the FIBA Intercontinental Cup title, after beating the defending champions of the FIBA Americas League, the Venezuelan club Guaros de Lara, by a score of 76–71. Three years later, Canarias also won the 2020 FIBA Intercontinental Cup title, after they defeated the defending champions of the Basketball Champions League, the Italian club Virtus Bologna, by a score of 80–72.

In March 2020, the club stopped the 2019–20 season due to the COVID-19 pandemic in Spain. The following season, the 2020–21 season, was the most successful season in the ACB in the team's history. After finishing third in the regular season, Canarias beat San Pablo Burgos before being eliminated in the semi-finals by Barcelona. In the 2021–22 season, Canarias won their second BCL championship after defeating fellow Spanish team Manresa in the final in Bilbao.