The phenomenon of many-body Stark localization of bosons in tilted optical lattice is studied. Despite the fact that no disorder is necessary for Stark localization to occur, it is very similar to well-known many-body localization (MBL) in sufficiently strong disorder. Not only the mean gap ratio reaches Poissonian value as characteristic for localized situations, but also the eigenstates reveal multifractal character as in standard MBL. Stark localization enables a coexistence of spacially separated thermal and localized phases in the harmonic trap similarly to fermions. Stark localization may also lead to spectacular trapping of particles in a reversed harmonic field which naively might be considered as an unstable configuration.