Morrow graduated from the newly founded University of California, Berkeley architecture program in 1906. He then attended Ecole des Beaux-Arts in Paris from 1908 until 1911. He moved back to Oakland and began practicing architecture in San Francisco and Oakland. He designed houses, banks, theatres, hotels, schools, and commercial buildings. He married Gertrude Comfort Morrow, a fellow architect and UC Berkeley graduate. He worked with Gertrude and architect William I. Garren, and with them designed the Alameda-Contra Costa County Building for the 1939 Golden Gate International Exposition.  Morrow and his associates also designed the rectory and guest house of the Mission San Juan Bautista.
Morrow was hired in 1930 by Joseph Strauss to design the Golden Gate Bridge. Morrow collaborated with Strauss with the design, sketching his ideas in charcoal. Morrow romanticized the bridge long before he was hired to work on it, writing in 1919 that "The narrow strait is caressed by breezes from the blue bay throughout the long golden afternoon, but perhaps it is loveliest at the cool end of the day when, for a few breathless moments, faint afterglows transfigure the gray line of hills." 
As well as the overall design, Morrow designed smaller features of the bridge such as the railing and walkways and streetlamps. He also added the vertical fluting to the bridge, a stylized geometry in the era's Art Deco style. The design caught the bay light throughout the day, creating dramatic, changing shadows and contributing to the public's view of the bridge as a sculpture as much as a roadway.
It was also Morrow that decided the bridge should be painted international orange. At first, Morrow's suggestion was deemed by the bridge authorities as ludicrous, as it was thought no paint could withstand the salty weather. Morrow found such a paint, and the bridge authorities relented.
Morrow was a member of the American Institute of Architects and the American Society of Landscape Architects, an editor of Pacific Coast Architecture, and a contributor to the Architectural Record and urian samplesvarious other periodicals. He served as chairman on the Section on Architecture of the Commonwealth Club of California, and director fo the American Historical Building Survey.