I don't know the appropriate setup to encrypt whole disk drive using FileVault 2 and Automatically backup it without issues. Currently, I'm using a 2nd-gen Intel i7 MBP running macOS High Sierra 10.13.6 (17G5019), One Internal Crucial SSD, APFS volume, and using Time Machine for Backup on a G-technology External Drive, Mac OS Extended (Journaled).

/dev/disk0 (internal, physical):
#:                       TYPE NAME                    SIZE       IDENTIFIER
0:      GUID_partition_scheme                        *500.1 GB   disk0
1:                        EFI EFI                     209.7 MB   disk0s1
2:                 Apple_APFS Container disk1         499.9 GB   disk0s2

/dev/disk1 (synthesized):
#:                       TYPE NAME                    SIZE       IDENTIFIER
0:      APFS Container Scheme -                      +499.9 GB   disk1
                             Physical Store disk0s2
1:                APFS Volume Macintosh HD            456.0 GB   disk1s1
2:                APFS Volume Preboot                 20.4 MB    disk1s2
3:                APFS Volume Recovery                512.0 MB   disk1s3
4:                APFS Volume VM                      10.7 GB    disk1s4

/dev/disk2 (external, physical):
#:                       TYPE NAME                    SIZE       IDENTIFIER
0:      GUID_partition_scheme                        *4.0 TB     disk2
1:                        EFI EFI                     209.7 MB   disk2s1
2:                  Apple_HFS G-DRIVE USB             4.0 TB     disk2s2
3:       Microsoft Basic Data G-UTILITIES             4.1 GB     disk2s3

You can enable FileVault 2 from System Preferences > Security & Privacy > FileVault. Just press "Turn on FileVault..." and full disk encryption will be setup.

Full Disk Encryption in this sense means that all your own data on the Macintosh HD file system will be encrypted. There is a preboot partition that isn't encrypted, as this is where the software necessary to decrypt the drive is stored. Without it, you wouldn't be able to boot the Mac.

When you plugin the USB drive, macOS will ask you if you want to use it for backups. If you confirm that, it will ask you whether or not you want the backups encrypted. Set the checkmark and encryption of the backup will automatically be setup for you.

If you have already started backing up to the external disk without encryption, you can enable encryption afterwards like this:

Open System Preferences > Time Machine. Click "Select Disk..." and remove the external disk.

Do it again and select the disk again, and it will ask again for encryption. Set the checkmark and you'll be asked to set a password. The disk will then be encrypted. The backups already stored on the drive will be preserved.

  • Note that encryption of the startup disk and the backup disk are completely independent -- one can be encrypted and the other not, and if they're both encrypted the passwords have no connection to each other. – Gordon Davisson Mar 21 at 0:42

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