There is wide variation in brain shape among birds. Differences in brain dimensions reflect species-specific sensory capacities and behavioral repertoires that are shaped by environmental and biological factors during evolution. Most previous studies aimed at defining factors impacting brain shape have used volumetric or linear measurements. However, few have explored the quantitative indices of three-dimensional (3D) brain geometry that are absolutely imperative to understanding avian evolutionary history. This study aimed: (i) to explore the relationship between brain shape and overall brain size; and (ii) to assess the relationship between brain shape and orbital shape. Avian brain endocasts were reconstructed from computed tomography images and analyzed using 3D geometric morphometrics. Principal component analysis revealed dominant regional variations in avian brain shape and shape correlations between the telencephalon and cerebellum, between the cerebellum and myelencephalon, and between the diencephalon and optic tectum. Brain shape changes relative to total brain size were determined by multivariate regression analysis. Larger brain size was associated with a relatively slender telencephalon and differences in brain orientation. The correlation between brain shape and orbital shape was assessed by two-block partial least-squares analysis. Relatively round brains with a ventrally flexed brain base were associated with rounder orbits, while narrower brains with a flat brain base were associated with more elongated orbits. The shapes of functionally associated avian brain regions are correlated, and orbital size and shape are dominant factors influencing the overall shape of the avian brain.