Given that Fallout already has a Commonwealth, it only makes sense that they have a Prime Minister to go with it.
The former Prime Minister was added into Fallout 4 a couple of years ago, although it appeared during the Christmas holidays so it flew under the radar. I can't find any listings on NexusMods or the Bethesda mods page, so it's more likely that Abbott found his way to post-apocalyptic Boston by way of the custom character creator.
SaturdayMorningStrategy posted a little story about Tony's time in the wasteland on Imgur, and you have to appreciate the likeness (even if the real Abbott isn't this ripped):
"Tony emerges from the vault, and the first thing he finds is a source of clean, green fusion cores," the description reads. "One day in office and he's already made a new mine!"
Good. Stick to character.
"Tony hasn't rebuilt the lodge yet, but the Red Rocket Truck Stop will have to for now."
Makes me wonder what other politicians have journeyed through the Commonwealth. Anyone want to mod Bronwyn Bishop in with a chopper?