He was born in México of very humble origin. His outstanding sensitivity was apparent early in life by his desire to study music and drawing. He studied at the Escuela Nocturna de Arte para Trabajadores No 1 (Art Night School for Workers No. 1). Under his teacher, Santos Balmori Picasso, Meza developed an exceptional talent and unique technique in drawing.
He mastered drawing with pastels using whites, greens, reds and yellows thereby defining a recognizable "Meza" style.
When Diego Rivera discovered Guillermo Meza in 1940, he arranged for Meza's first one man show which was held at the Galeria de Arte Mexicano. Meastro Meza participated in a large number of exhibits throughout México, the United States and Europe.
His works are in the collections of the Palacio Nacional de Bellas Artes (México ), Museo de Arte Moderno (México), Museum of Modern Art (New York), The Art Institute (Chicago), the University of Michigan (Ann Arbor), the San Francisco Museum of Art, the Dallas Museum of Art, Stanford University Art Gallery (Palo Alto), the Museum of Modern Art (San Juan, Puerto Rico), and the Philadelphia Museum of Art.