Start passive. Instruct the IT helpdesk to support employees who *want* to use Linux instead of Windows. There will always be some in every organisation. These are the very people you can trust not to blame Linux for the interoperability problems that will invariably ensue. Use them and the IT helpdesk to compile a list of the problems encountered and how they were solved.
You now have a list of things you need to do to support other users migrating from Windows to Linux, and you have obtained it "under the radar", without a lot of noise and publicly visible pain.
That's when you start the actual migration.