Although Tuxedo Mask never says the line “My job here is done” in the anime, the origin of the meme is a comic that consists of screenshots taken from episode Nakimushi Usagi no Kareinaru Henshint.
It was created to mimic the character’s overall personality, as he tends to exaggerate his importance in situations which he has little or no impact on. Usually this happens after Sailor Moon fights one of her enemies.
The comic was initially posted on Tumblr but since then it has been deleted.
However, it was a big success and hype started generating around the format. Reddit, 9gag and several other meme sharing sites featured the format.
Eventually, people started to implement My job here is done into real-life situations, utilizing the meme as an exploitable.