He learned to play the piano at the music high school of Cienfuegos. He studied medicine but abandoned his studies due to financial difficulties. He began playing with groups in Las Villas. In 1940, he moved to Havana, where he played in the charangas of Paulina Álvarez and Paulín, with Arsenio Rodríguez, Kubavana and Senén Suárez and in the big bands Siboney and Riverside. In 1943, he released his first recording, together with Arsenio Rodríguez. During the 50s, he served as a member of the Orquesta América, Orquesta de Enrique Jorrín and CMQ. Between 1957 and 1961, he worked in Venezuela. Soon he became known in Cuba and other parts of Latin America.
In the early 1960s Rubén became the pianist for the Orquesta de Enrique Jorrín, and would continue to play for him for the next 25 years. After Jorrín's death in 1987, Rubén briefly took over the role of band leader, but retired soon after.
González retired in the late 1980s, but after U.S.-musician Ry Cooder heard about him in 1996 he called to meet him despite false claims that Rubén could no longer play due to arthritis. After Ry Cooder's insistence to meet him, Rubén González (who up to this point had not owned a piano in approximately 11 years) started a second career in 1996 under Ry Cooder's wing. It was this same year when the solo album Introducing...Rubén González was recorded and released. The next year, Ry Cooder produced the Grammy winning Buena Vista Social Club, featuring González, Compay Segundo, Ibrahim Ferrer, Orlando "Cachaíto" López, Omara Portuondo, Eliades Ochoa among other veteran Cuban musicians, most of whom had careers and foundations that went back to the famous 1950s Havana scene. Wim Wenders filmed a documentary under the same name, and González and his colleagues became famous worldwide.
Introducing...Rubén González was recorded in the same sessions as Buena Vista Social Club, and Chanchullo was recorded and released in 2000. Both are on World Circuit Records.
González's last public appearances were in Mexico and Cuba in 2002.