Gribbroek was born in Rochester, New York. He studied at the Rochester Institute of Technology, the Pennsylvania Academy of Fine Arts and in the 1930s, at the University of New Mexico field school in Taos, and with Emil Bisttram at his Taos School of Art. In the early 1930s, Gribbroek was a commercial art director in Rochester for Hutchins Advertising Company, and from 1934 through 1935, was Art Director for the Rochester Museum and Science Center. Then he enrolled in the Art Students League in New York City, studying with Morris Kantor and Kimon Nicolaides. He was also a student of Donald Graham at the Art Center in Los Angeles, but the date is unknown.

In 1929, he began his visits to New Mexico where he lived "on and off" for several years at the Isleta Pueblo, in the Rio Grand Valley about 13 miles south of Albuquerque. There he met William Lumpkins and Brooks Willis, who were painting at the pueblo, and it was the beginning of a long friendship with Lumpkins, whom Gribbroek later introduced to Emil Bisttram. In 1936, Gribbroek moved to Taos and began study with Bisttram and through him, met Horace Towner Pierce and Florence Miller Pierce, husband and wife. These associations then led to Gribbroek's participation in establishing the Transcendental Painting Group (TPG) New Mexico's pioneering group of painters dedicated to abstraction.

In 1939 and 1940, Gribbroek was in Amarillo, Texas, teaching art and painting realistic portraits, which led his TPG friends in New Mexico fearing he had abandoned their mutual dedication to avant-garde style of abstraction and non-objective subject matter. However, by spring of 1940, he was back in Taos and committed to the TPG upcoming exhibition schedule. Few paintings of his from this period are extant, but apparently they were well received by his peers. TPG painter Alfred Morang was quoted in the Santa Fe New Mexican magazine, August 1938: "Robert Gribbroek, one of the best draftsmen in America, has a command of geometrical form second to few. . . .His works are startling in their exactness and precision [and] . . .touch on the order of the universe or planetary movement."

In the mid 1940s, Gribbroek worked as a technical illustrator for Douglas Aircraft in Los Angeles followed by employment with Disney Studios and then tradition for 18 years he was in Hollywood with Warner Brothers where according to some sources, (see addendum) he co-founded Looney Tune cartoons and served as studio Art Director. In this capacity, he created backgrounds for Tweety Bird, Sylvester the Cat and Roadrunner. Between 1941 and 1960, he continually returned to Taos "until he ran out of money". (Blankenship) Many people in that community regarded him as a celebrity because of his association with famous Hollywood personalities including Richard Burton with whom he was part of the cast of the movie Candy, and for his ventures such as raising chinchillas for the fur industry.

In New Mexico, Gribbroek was regularly active in the art community and exhibited paintings at the Museum of Fine Arts in Santa Fe and the Blue Door Art Gallery in Taos. In 1953, he joined the Taos Art Association. Between 1965 and 1970, he lived in Spain as an actor in TV commercials and films, but returned to Taos in August, 1970, the year before he died.

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