Hey there, SHAK007!
In order to be able to use the WD Passport on your Xbox 360 Elite, you'd need to format it in FAT32 file system. It offers the best compatibility for your gaming console and also allows you to use it with other operating systems (Windows OS and Mac OS). However, there are some limitations that come with this particular file system, you can read through this article from our knowledge base that explains them in detail:
http://products.wdc.com/support/kb.ashx?id=LAUXp1
As for the formatting procedure itself, yes, you can do it through Windows 10's Disk Management as well. Here is a tutorial that can walk you through it:
How to partition and format your HDD:
http://products.wdc.com/support/kb.ashx?id=kB3iMy
Just make sure you select the FAT32 File System from the Wizard, instead of the default NTFS.
Hope this helps you. Let me know if you need further assistance!
SuperSoph_WD