The viscosity of gelatin methacryloyl (GelMA)-based bioinks generates shear stresses throughout the printing process that can affect cell integrity, reduce cell viability, cause morphological changes, and alter cell functionality. This study systematically investigated the impact of the viscosity of GelMA-gelatin bioinks on osteoblast-like cells in 2D and 3D culture conditions. Three bioinks with low, medium, and high viscosity prepared by supplementing a 5% GelMA solution with different concentrations of gelatin were evaluated. Cell responses were studied in a 2D environment after printing and incubation in non-cross-linked bioinks that caused the gelatin and GelMA to dissolve and release cells for attachment to tissue culture plates. The increased viscosity of the bioinks significantly affected cell area and aspect ratio. Cells printed using the bioink with medium viscosity exhibited greater metabolic activity and proliferation rate than those printed using the high viscosity bioink and even the unprinted control cells. Additionally, cells printed using the bioink with high viscosity demonstrated notably elevated expression levels of alkaline phosphatase (ALP) and bone morphogenetic protein-2 (BMP-2) genes. In the 3D condition, the printed cell-laden hydrogels were photo-cross-linked prior to incubation. The medium viscosity bioink supported greater cell proliferation compared to the high viscosity bioink. However, there were no significant differences in the expression of osteogenic markers between the medium and high viscosity bioinks. Therefore, the choice between medium and high viscosity bioinks should be based on the desired outcomes and objectives of the bone tissue engineering application. Furthermore, the bioprinting procedure with the medium viscosity bioink was used as an automated technique for efficiently seeding cells onto 3D printed porous titanium scaffolds for bone tissue engineering purposes.