Supported lipid bilayers on solid surfaces have promising potential for diverse applications, such as separation processes, biosensors, drug delivery, and more. However, the self-assembly of supported lipid bilayers via vesicle fusion—the commonly used preparation method for these lipid bilayers—is not fully understood. It is often found that lipid bilayers are patchy or exhibit holes/defects, which may hinder their applicability. Moreover, it is not fully understood whether these holes are transient, kinetically trapped, or thermodynamically stable (long-lasting). Here, we derived equations to quantitatively describe the mechanism of vesicle fusion on atomically smooth hydrophilic surfaces. The derived equations determine whether defectless lipid bilayers are thermodynamically stable/favorable and qualitatively predict the self-assembly rate. It is shown that vesicle fusion is governed by van der Waals and double layer interactions, as well as undulation repulsion between the lipid bilayers and the solid surface. Utilizing various experimental techniques, we confirmed the equation predictions by studying the self-assembly of lipid bilayers on silicon wafers using lipid mixtures that exhibited different electric potentials. Furthermore, we found that cholesterol increases the lipid bilayer resistivity—a crucial parameter for several applications—and the rate of self-assembly, by decreasing both the dielectric constant of the lipid bilayer and the undulation repulsion between the lipid bilayers and the solid surface. The derived equations can be used as quantitative guidelines for designing supported lipid structures on the surface, such as a layer of intact lipid vesicles, patchy or defectless lipid bilayers.