CB Gran Canaria was founded inside Claret School and for many years played under that denomination. Following a successful period in school competitions, a senior team was created and integrated on the Spanish Second Division. The team played in that division until 1984, when the team adopted the decision of having a statute of its own, therefore becoming an independent institution. The new statute was approved on May 22, 1985 and the team became Claret Club de Baloncesto.
The following years, the team moved many times between Liga ACB and 1st Division B. On the 1987–88 season the club changed its name to CB Gran Canaria, paying homage to the place where its social mass came from. On 30 June 1992 the team became a sports public limited company (Sociedad Anónima Deportiva, SAD in Spanish) in order to fulfil with the requirements of the then-new Spanish sports legislation.
After three seasons in the Spanish silver division the team won the first Liga EBA in the 1994–95 season and was promoted to Liga ACB. From that season on, CB Gran Canaria has stayed in the top level of the Spanish basketball. The 2012–13 represents the team's eighteenth consecutive season in Liga ACB.
In April 2015, Gran Canaria played the Eurocup Finals. The team was defeated by BC Khimki in the two legs. Ten months later, the club qualified for the first time to a final of a national trophy. In the 2016 Copa del Rey defeated Valencia Basket in the quarterfinals and Dominion Bilbao Basket in the semifinals, but could not beat Real Madrid in the final, where it lost by 81–85.
On 24 September 2016, Gran Canaria won its first national title after beating FC Barcelona 79–59 in the Final of the 2016 Supercopa played in Vitoria-Gasteiz.
One season later, in June 2018, Gran Canaria qualified for the second time to the league semifinals and also achieved qualification to the EuroLeague for the first time ever.