González has been married four times. He was married to Puerto Rican volleyball player Elaine López, sister of fellow major leaguer Javy López, during the early 1990s. This marriage broke down when a local newspaper released a cover photo of singer Olga Tañón kissing González during a concert in San Juan. A scandal followed, with González divorcing Elaine López and marrying Tañón, who said she had no idea González was married to Lopez when she kissed him. González and Tañon had a daughter together, Gabriela González Tañón, in 1998. González and Tañon divorced less than two years later. His daughter later became one of only fifty people in the world (and the first Puerto Rican) ever to have been diagnosed with Sebastian syndrome, a mild blood clotting disorder.