Yes. Any Canon lens with the letters "EF" in it's name will work on your camera. Lenses with EF-S will not.
The Canon EF 35-350mm f/3.5-5.6 USM L is one of the extreme range zooms made by Canon. A real blast from the past. The lens is from 1993. This lens was popular with the press. It is discontinued now. It has been replaced by the EF 28-300mm f/3.5-5.6 USM L IS.
EB
EOS 1D, EOS 1D MK IIn, EOS 1D MK III, EOS 1Ds MK III, EOS 1D MK IV and EOS 1DX and many lenses.
