Lenses from a 35mm canon camera fit on a canon eos digital camera?

Yes, with the right mount adapter.

Canon EF lenses were introduced in 1987 for Canon's new EOS auto-focus cameras. All EF lenses fit all EOS film and digital cameras.

Some Canon DSLR cameras, such as the digital Rebels, have an APS-size (smaller) sensor. These cameras can use EF lenses with full automation, and can also use the EF-S lenses designed especially for them. The advantage of EF-S lenses is that they are more compact than EF lenses. The EF-S lenses will only work on some Canon DSLR bodies, so compatibility should be determined before purchasing an EF-S lens.