Last updated on December 7th, 2016 at 12:39 pm.
A good question.
I recently needed to move my iCloud connected Apple Photos library to an external hard drive as it was taking up too much space on my laptop. Since I was doing that anyway I decided to also put it in my Dropbox so that I could get an extra backup of it as well.
If you just move the library and then delete it, Apple Photos tends to not like you too much. Apple has made it possible to move the location fairly easily though, you just need to do the steps in the right order. Here is the process I used.