Apple - Enabling Time Machine for a USB HDD with NTFS

You can't backup to an NTFS formatted disk as stated below:

Note: Every available disk that can be used to store backups is listed. If you’ve partitioned a disk, the available partitions are listed. Time Machine can’t back up to an external disk that's connected to an AirPort Extreme, or to an iPod, iDisk, or a disk formatted for Microsoft Windows (NTFS or FAT format). If you select an NTFS or FAT-formatted disk, Time Machine prompts you to reformat the disk. Choose a different disk or reformat the disk in Mac OS Extended (Journaled) format. Because reformatting erases any files on the disk, only do this if you no longer need the files or if you have copies of them on a different disk.

This quote is from the apple support page for Time Machine

You could always reformat the disk in Mac OS Extended (Journaled) format which would allow you to use it.

You can backup to an NTFS-formatted volume.

I backed up my Mac (Yosemite) with Time Machine as per Graham's answer here (https://apple.stackexchange.com/a/57082/134740), but I had to use a .sparseimage, as a .sparsebundle image failed to be created on the NTFS volume – for details on the differences between the two, see: https://support.apple.com/kb/PH22247.

In terms of restoring that image for recovery purposes, I tested it by restarting and holding the keys Cmd+R to boot into Mac OSX Recovery (https://support.apple.com/en-ie/HT201314) and Time Machine could not find the disk. I had to start Disk Utility, mount the image manually, then go back to Time Machine and it could see the volume and all the available backups in it.

I didn't actually go ahead and start the restore but I assume if it can see the backups, it should be able to restore them : )