We present a joint theoretical/experimental study of a van der Waals heterobilayer with type-I band alignment formed by monolayers of WSe2 and MoTe2. Our first-principles computation suggests that both the valence band maximum and the conduction band minimum of the WSe2/MoTe2 heterobilayer reside in the MoTe2 layer. The type-I band alignment allows efficient transfer of excitons from WSe2 to MoTe2. Since monolayer MoTe2 is a direct semiconductor with a bandgap in the infrared range, this heterobilayer is attractive for infrared light emission applications. Time-resolved measurements of photocarrier dynamics were conducted to provide experimental evidence of the type-I nature of this heterobilayer. In these measurements, we found that excitation energy can transfer from WSe2 to MoTe2 efficiently, but not along the opposite direction. The efficient energy transfer can serve as an optical gain or wavelength conversion mechanism for efficient emission from MoTe2, which can be utilized in ultrathin and efficient infrared light sources.