Very likely yes. But you'll need the appropriate "adapter" for that. Some camera makers have optional adapters for lenses outside their own (e.g. Fujifilm and Panasonic have Leica M adapters); some only have adapters for their own lenses (e.g. Canon, Nikon, Sony). Fortunately, third party makers such as FotodioX, Metabones, Novoflex, and Sigma have been filling in all the gaps.
But...you need to be aware of a number of things that might arise:
- Automatic features (focus, VR, etc.) don't always work, or don't work as reliably as they did on the original camera.
- You may be restricted to certain exposure modes (typically manual exposure mode) and features on the camera.
- You may have to set something on the camera (e.g. "Shoot without lens" setting on some models, non-CPU Lens Data on Nikons).
- Manual focus lenses are still manual focus. Different cameras have varying focus aids to help, while some have none.
- You have to be aware of the crop factor: a 50mm lens on most mirrorless cameras is a telephoto, not a normal lens.
- The lenses may be a lot bigger than the camera, especially since they were designed to be used on a deeper camera in the first place, plus the adapter sticks out from the camera, too.
- Not all older lenses perform great on newer digital cameras, this is particularly true of wide angle lenses and BSI sensors.
That said, many of us use our older lenses quite successfully on our mirrorless cameras.
So far, the best of the bunch in terms of adapting a DSLR lens to a mirrorless camera tends to revolve around Canon EF lenses mounted on Sony E/FE cameras. That's probably because the Canon EF lens mount is well known through reverse engineering, and the Sony mirrorless mount specifications were available to partners who signed a license agreement. Still, while I've heard some "rave" about how well their EF lens works on a Sony A7 body, my experience says you're still better off with a native FE lens.
See this article on adapting lenses.