A three-dimensional phase-field model has been developed for studying the stability and evolution of coherent microstructure evolution in thin films constrained by a substrate. Elastic solutions are derived for both elastically anisotropic and isotropic thin films with arbitrary domain structures, subject to the mixed surface stress-free and substrate constraint boundary conditions. Electric field in the film is calculated taking into account the long-range electric dipole-dipole interactions under short-circuit, open-circuit or mixed electric boundary conditions. A specific example of a [001] orientated PbTiO3 film heteroepitaxially grown on a [001] cubic substrate is considered. We investigated the effect of substrate constraint, temperature and depolarization on the volume fractions of ferroelectric domain variants, domain-wall orientations, surface topology, domain shapes, and their temporal evolution for a cubic-to-tetragonal ferroelectric phase transition. It is shown that the shapes of a-domains with tetragonal axes parallel to the film surface are significantly different from those of c-domains with tetragonal axes perpendicular to the film surface. For the substrate constraints and temperatures under which both a1- and a2-domains coexist, both types of a-domains are present with their tetragonal axes perpendicular to each other, and the domain wall orientations deviate from the 45 degree orientation generally assumed in thermodynamic analyses. It is demonstrated that a substrate constraint results in sequential nucleation and growth of different tetragonal domains during a ferroelectric phase transition. The effect of depolarization on the domain shape and domain variant volume fraction will be discussed.