Homar was born on September 10, 1913, in San Juan to Lorenzo Homar and Margarita Gelabert, who had emigrated to Puerto Rico from Spain. His family valued art and had artistic inclinations. His father was a film distributor in Puerto Rico and his mother was a pianist.
As a young child Homar attended schools in Spain, where his parents relocated briefly during his childhood, and also attended local schools in his native San Juan. When he was 15 years old, his family moved to New York. Their arrival in New York coincided with the Great Depression and Homar was forced to leave school and go to work in order to help support his family. Meanwhile, he continued pursuing his interests in the arts and received athletic training as a gymnast and acrobat at the YMCA. While he would have liked to become a musician, the lack of economic resources hindered him from receiving musical training at an early age. In 1931, Homar enrolled in New York's Art Student's League.
He was taught by the noted artist George Bridgeman, who encouraged Homar to expose himself to as many artistic influences as possible in order to develop an artistic style of his own. While continuing with his athletic interests, Homar focused on the development of his artistic abilities. By 1937 he had become an apprentice at the internationally known jewelry company Carder. Working with one of their master designers, Ernest Loth, Homar acquired key engraving skills that he used later in the development of his own art. After he finished his training he continued to work for Carder and took some courses at Pratt Institute in New York.
World War II interrupted his career. Homar volunteered for the war effort and joined the U.S. armed forces. He traveled the Orient, earning a Purple Heart after being wounded in conflict. On returning from the war, he resumed his career at Cartier and attended art classes offered at of the Brooklyn Museum of Art. While there, Homar was taught by some of the most accomplished artists of the time, such as Mexican muralist Rufino Tamayo, Ben Shahn, Arthur Osver, and Gabor Peterdi.
In 1950 Homar returned to Puerto Rico, where his career as an artist quickly developed and flourished. From the moment of his arrival, Homar and his art have been a constant in the artistic circles of Puerto Rico. In that year he had his first successful art exhibit at the Puerto Rican Athenaeum, one of the leading artistic and intellectual organizations on the island. That same year, he helped to establish the Center for Puerto Rican Arts, an organization that provided opportunities for Puerto Rican artists.
One of Homar's first and most important experiences in Puerto Rico was his work within the Community Education Division of the Puerto Rico Department of Education (DIVEDCO). Former governor Luis Muñoz Marín had established this department in 1949 to aid community development for poor Puerto Ricans. Through distribution of educational materials such as films, booklets, and posters, DIVEDCO launched broad initiatives to assist and educate poor Puerto Ricans. When Homar first joined the DIVEDCO in 1951, he worked as a poster-maker and illustrator for many of the projects in development. Some of his co-workers were talented artists who were beginning their artistic careers and who later became some of the most notable Puerto Rican artists and intellectuals of the time. Among them were filmmaker and photographer Jack Delano, writers José Luis González and Pedro Juan Soto, and fellow graphic artists Rafael Tufiño and Isabel Bernal. Homar was promoted to head of the graphic arts department in 1952.
Throughout the 1950s, Homar continued a process of rich artistic production. His engravings of native Puerto Rican images were widely acclaimed by art critics and collectors. The posters that he created to promote films, books, and projects at DIVEDCO have become unique historic testimonials to the legacy of this organization. His colorful posters are filled with rich images blended with fine engravings and calligraphy. Homar's ability to capture Puerto Rican realities through his work and to beautifully represent Puerto Rican history, culture, and social realities have made him the leader and one of the most important figure in the development of the poster as a medium of artistic, educational, and political expression. Equally important, as head of DIVEDCO, Homar encouraged and helped to launch a unique artistic ferment in the Puerto Rican arts establishment. Through his work and through his support of other artists he assisted in recreating and reclaiming the richness and uniqueness of Puerto Rican heritage and culture.
In 1957 Homar received a Guggenheim Fellowship and was asked by the government to organize the Graphic Arts Workshop at the Institute of Puerto Rican Culture. Once again, Homar helped to build another venue to teach art and pro-mote and encourage the talents of scores of Puerto Rican artists. He served as the workshop's director until he retired in 1973.