Although this is now a three-year-old thread, I found this advice very useful, even on macOS Sierra. I was trying to do an encrypted Time Machine backup to a 2 TB external USB drive, fresh out of the box (and apparently not encrypted from the get-go), from a MacBook Pro 13" 2016 model. The Time Machine backup itself (about 200 GB) took maybe three hours... but as for the encryption, even after half a day the display still showed only 10% finished. I was wondering whether I really needed to let the computer grind away at encryption for a full week!
I took your advice and stopped the backup, reformatted the external drive in Disk Utility as encrypted, and then reassigned the disk as a Time Machine backup. The backup and encryption took perhaps three hours tops!
All I can assume is that formatting the disk first as encrypted using Disk Utility and then doing the Time Machine backup saved the step of macOS actually encrypting every single byte on an already-formatted hard disk, even though the lion's share of that hard disk was empty. Format and encrypt first, then do the backup... that seems the most efficient way, it appears.
Thanks again for the great tip!
Jeff