The clip, shared widely on social media, includes clips of Charles III and other members of the royal family in a parody of the show's opening theme song.
Along with clips of Queen Consort Camilla laughing, Prince William running, Kate Middleton and their three children, the credit "starring King Charles III" appears on screen as the theme song plays.
The sitcom aired from 1984 to 1990 in the US, following the life of a young college student who boards with a family and looks after the three children while their parents are working.
Twitter users have welcomed the meme, with one commenting on the footage, "Thank you. That's phenomenal and made my day."
Another wrote, "Everyone stealing my jokes, but with far better production value."
"Ok, it's kinda funny… even endearing. American memes take on King Charles," another commented.
It's not the only meme about the new King to go viral online.
And while some of them have raised eyebrows for circulating so soon after the Queen's death, others grieving around the world have welcomed a bit of light relief.
One of the most popular notes that Charles has just got his start as King at 73, proving it's never too late to follow your dreams.
Another called Charles "the artist formerly known as Prince" - noting his title change in a nod to the iconic artist.
And who can forget the viral moment of Charles' frustration with a pen? Footage of him losing his temper with a faulty ink pen quickly went viral as he was filmed during a signing ceremony.
And it wasn't his first run-in with troublesome stationery. During his official assession ceremony over the weekend, a clip of Charles gesturing at his aides to clear his desk went viral.
Royal fans were quick to take to Twitter to make light of the situation with one person saying, "Charles' brief fury at the pen tray is definitely the highlight of this for me."
Another, sympathetic to the King's recent loss, said, "Prob v stressed to be fair."
