Cantú Garza was son of the physician Adolfo Cantú Jáuregui and his wife, the writer María Luisa Garza aka "Loreley". He visited the open air painting school of Coyoacán, and traveled to Europe and the United States from 1924 until the mid 1930s. During this time, he lived in the Rue Delambre inMontparnasse from 1924 to 1934. He exhibited in the Exposition Park Museum in Los Angeles, California in 1929, and his wife Luz Fabila spent her academic years with Frida Kahlo from 1922 to 1924. Cantú developed a close friendship to André Breton, Mateo Hernandez, Lino Enea Spilimbergo, Renato Leduc, Antonin Artaud, José Moreno Villa, Jean-Emile Puiforcat and Luis Cardoza y Aragón. In 1934 the Galería de Arte Mexicano showed works of the Big Three Mexican muralists (Spanish: Los Tres Grandes) Diego Rivera, José Clemente Orozco, and David Alfaro Siqueiros as well as those of Jean Charlot,Roberto Montenegro, Rufino Tamayo, and of him. In contrast to the Tres Grandes, who were identified with the period for the most time of their artists' lives, the painters Alfredo Ramos Martínez, Jorge Juan Crespo de la Serna, Jean Charlot, Francisco Cornejo, Luis Ortiz Monasterio, José Chávez Morado and Federico Cantú lived, studied, taught, and worked in Los Angeles and New York (1929–1942). In 1939 Cantú joined the Perls art gallery that had recently been opened in New York. By 1940 Cantú became a favorite of the American art collector MacKinley Helm. Mac began acquiring his drawings and paintings and exhibiting them in Metropolitan Museum, Santa Barbara Museum, Philadelphia Museum.During these years. After 1943 Garza taught at "La Esmeralda", and studied engraving under Carlos Alvarado Lang in 1945. After 1949 he taught at University of California. After 1951 he devoted himself mainly to painting murals in private homes. In 1960 he began producing reliefs and emblematic sculpture of the Mexican Institute of Social Security (IMSS) & Loteria Nacional  . He created his last monument, a memorial to Alfonso Reyes, in 1988.
His murals decorate monuments, public buildings and universities. His mural "El flechador del sol" (1961) has a total surface of 650 sqm. He is also the author of the mural of the Universidad Autónoma de Nuevo León (UANL) Capilla de la Universidad UIC, La Purísima NL Monterrey es:Iglesia de la Purísima (Monterrey). His works were exhibited in notable galleries, for example in the Tate Gallery and in the Perls Galleries, , as well as in the Museum of Modern Art. "Gloria and tristemente" (CYDT collection) and his nude "Mujer Desnuda" were sold at Sotheby's in 2005.