We present measurements of morphological parameters from fitting 53,885 galaxies detected to a magnitude limit of F356W < 28.5 in the CEERS NIRCam imaging with GALFIT in six broadband filters: F115W, F150W, F200W, F277W, F356W, and F444W. We provide a public catalog of Sérsic indices, effective semimajor axes, axis ratios, integrated magnitudes, and position angles for these galaxies in each of the filters. Uncertainties in the measured parameters are estimated from simulated galaxies that have similar noise and background properties as the observed galaxies. We compare our measurements with those in the CANDELS/Extended Groth Strip field measured with Hubble Space Telescope/WFC3 and find that the sizes agree to within 0.09 dex and the Sérsic indices agree to within 0.13 dex. We further present the evolution in the size─mass relation, and find that the evolution to z ∼ 9 is consistent with previous results derived at lower redshift. Finally, we look at the color gradients of galaxies at 1 < z < 5 and find that for late-type galaxies (n < 2.5), there is a strong dependence on mass, but no apparent evolution with redshift, indicating that the stellar populations and dust attenuation in more massive galaxies vary substantially with radius and contribute to significant morphological k-corrections. For early-type galaxies (n > 2.5), the color gradients are nearly flat with no dependence on mass, indicating that the stellar populations are more uniform throughout. The structural measurements presented are accurate to 20% or better for most galaxies with F356W < 27.0 mag and will enable further studies of galaxy morphology to z ∼ 10.