Quantum systems in confined geometries are host to novel physical phenomena. Examples include quantum Hall systems in semiconductors1 and Dirac electrons in graphene2. Interest in such systems has also been intensified by the recent discovery of a large enhancement in photoluminescence quantum efficiency3,4,5,6,7 and a potential route to valleytronics6,7,8 in atomically thin layers of transition metal dichalcogenides, MX2 (M = Mo, W; X = S, Se, Te), which are closely related to the indirect-to-direct bandgap transition in monolayers9,10,11,12. Here, we report the first direct observation of the transition from indirect to direct bandgap in monolayer samples by using angle-resolved photoemission spectroscopy on high-quality thin films of MoSe2 with variable thickness, grown by molecular beam epitaxy. The band structure measured experimentally indicates a stronger tendency of monolayer MoSe2 towards a direct bandgap, as well as a larger gap size, than theoretically predicted. Moreover, our finding of a significant spin-splitting of ∼180 meV at the valence band maximum of a monolayer MoSe2 film could expand its possible application to spintronic devices. The transition from an indirect to direct bandgap in transition metal dichalcogenides has been observed in samples with thicknesses ranging from 8 to 1 monolayers by angle-resolved photoemission spectroscopy.