From: Филимон Лаковид on
In general: a DX lens mounted on a FF camera will typically result in
vignetting under at least some condition (apperture/focal lenght
combination). The other way round, i.e. mounting a FF lens on a DX
camera is no problem.

Canon specific: Any EOS-lens can be mounted on any EOS-camera. However
the EOS system (using the EF mount) is completely incompatible to the
earlier FD mount system.