Since the late sixties, Rufino Tamayo (Oaxaca, 1899 - Mexico City, 1991) began acquiring works to form a collection of international contemporary art. The artist donated this collection with the aim of providing the Mexican public with an approach to the 20th-century art and, with the same goal, promoted the creation of the Museo Tamayo, which would house this collection. He worked closely with the architects Abraham Zabludovsky and Teodoro González de León in the design and construction of the museum. The building was planned and considered as another piece of the collection since the beginning. On May 29, 1981, this cultural venue was inaugurated with the sponsorship of Grupo Alfa and the Televisa Cultural Foundation.
Five years later, the museum became part of the national heritage under the administration of the National Institute of Fine Arts, with a reopening on September 9, 1986. In that year, with the purpose of supporting the museum for its optimal functioning, Olga and Rufino Tamayo created the foundation that bears their names: Foundation Olga and Rufino Tamayo. Rufino Tamayo died a few years later (1991) leaving the museum in the hands of a union of both public and private actors who have guaranteed the continuity of the project over the years. The vocation of contemporaneity and openness to the world that encouraged Tamayo remain in force in the commitment to maintain the presence of the museum in the international contemporary art scene.