There are many many posts about this, so I will submit the fix that worked for me in several threads in the hope that it helps people:
I was struggling yesterday, and was having very mixed results ranging from handoff not working at all to it working on my iPhone only. I found an article offering a suggested fix, and it worked for me.
It appears to me that the "missing link" is the FaceTime setup (this was the only article I found that referenced FaceTime settings).
In my case, I had to sign into FaceTime using my AppleID (which I believe was set in the past, possibly disconnected at some point). Anyhow, it does make sense that this would be a potential gap in Handoff functioning, and it corrected my issue immediately.
Good luck...this is clearly not an example of "it just works".
The full article can be found at:
http://www.ibtimes.co.uk/continuity-calling-handoff-not-working-ios-8-try-out-fix-1466213
Step-1: Open the Settings app on your device running iOS 8
Step-2: Click General
Step-3: Click Handoff & Suggested Apps
Step-4: Turn Handoff option Off and turn it On again
Step-5: Tap General at the top of return to the previous menu
Step-6: Tap Settings at the top of return to the previous menu
Step-7: Tap FaceTime
Step-8: Put the iPhone Cellular Calls option Off and then put it back On again
Step-9: Once the action is completed, reboot the iPhone or the iPad