Indium selenide (InSe) and gallium selenide (GaSe), members of the III-VI chalcogenide family, are emerging two-dimensional (2D) semiconductors with appealing electronic properties. However, their devices are still lagging behind because of their sensitivity to air and device fabrication processes which induce structural damage and hamper their intrinsic properties. Thus, in order to obtain high-performance and stable devices, effective passivation of these air-sensitive materials is strongly required. Here, we demonstrate a hexagonal boron nitride (hBN)-based encapsulation technique, where 2D layers of InSe and GaSe are covered entirely between two layers of hBN. To fabricate devices out of fully encapsulated 2D layers, we employ the lithography-free via-contacting scheme. We find that hBN acts as an excellent encapsulant and a near-ideal substrate for InSe and GaSe by passivating them from the environment and isolating them from the charge disorder at the SiO surface. As a result, the encapsulated InSe devices are of high quality and ambient-stable for a long time and show an improved two-terminal mobility of 30-120 cm V s as compared to mere ∼1 cm V s for unencapsulated devices. On employing this technique to GaSe, we obtain a strong and reproducible photoresponse. In contrast to previous studies, where either good performance or long-term stability was achieved, we demonstrate a combination of both in our devices. This work thus provides a systematic study of fully encapsulated devices based on InSe and GaSe, which has not been reported until now. We believe that this technique can open ways for fundamental studies as well as toward the integration of these materials in technological applications.