Founded in 1995 as Soto de la Moraleja Club de Fútbol, Alcobendas first reached the fourth division in 2006–07, finishin...g in fourteenth position. Changing its name to Soto de Alcobendas Club de Fútbol in 2005, the team was again renamed the following year, to Alcobendas Sport, with the intention to cover the entire city.
In April 2020, Alcobendas announced an agreement with CF Rayo Majadahonda, and changed name to CD Paracuellos Antamira.[4] On 30 May 2023, their affiliation link ended, with Rayo Majadahonda choosing CU Collado Villalba as their new reserve team.
In August 2023 a Mexican group of investors bought the club to launch the project called México F.C. and are competing in the 3RFEF for the second season in a row.