Alexander Brook was born in Brooklyn, New York. As a young man, he gained his artistic studies at the Art Students League during 1914-1918. Brook studied with John C. Johansen, Frank V. DuMond, George Bridgeman and became acquainted with fellow artists Reginald Marsh, Yasuo Kuniyoshi, among others. These artists formed a movement of art known as American Realism. A member of the Society of Independent Artists, Brook and his colleagues refused to be part of the National Academy of Design.

During the Great Depression, Brook traveled and worked throughout the South, including Georgia and Florida. He began exhibiting his work in New York at the Downtown Gallery the National Academy of Design, Rehn Gallery, Knoedler, and the Carnegie Institute International Exhibition of Modern Painting (1930). He also began teaching at the Art Students League.

Brook was a primarily an realist painter who refused to adopt Abstract Expressionism during the post-war period. His works consist of figurative work, still-lifes, and landscapes, and figures, often of women. He later traveled to Europe, where he was influenced by the works of Picasso, Goya.

Brook lived in the Los Angeles area and exhibited at the Los Angeles County Museum of art. He became a member of the San Francisco Art Association and received awards at the Art Institute of Chicago (1929), the Pennsylvania Academy (1931), the Guggenheim Fellowship (1931).