After graduating from Yale Univeristy in 1901, Meeks began studying architecture at Columbia University. In 1904 he enrolled in the Ecole des Beaux-Arts in Paris after which he returned to the United States where he joined the architectural firm of Carrere and Hastings in New York. He was appointed professor of architecture at Cornell University, Ithaca, New York, in 1914, but two years later he joined the faculty of Yale, an institution with which he was affiliated until his retirement in 1947. In 1922, he was named Dean of the Yale University School of Fine Arts.
During the following years, Meeks became one of the most prominent architects on Yale's faculty and, during the 1920s and '30s, his students won many national and international awards. From 1929 to 1940, he served as director of the Yale Art Gallery.