There is not going to be a sequel, reboot, or spin-off of Full House. Sorry. Repeat: There is no official news of any sort of a Full House follow-up series in the works.
How did the hoax happen? Entertainment LiveJournal Oh No They Didn't!picked up the story on Monday.
Oh No They Didn't copied and pasted the entire article from a blog called Disney Treasures.
And that blog had copied and pasted the article from Screen Rant, which explains at the very top that the whole thing was an April Fool's joke from earlier this year.
Both Oh No They Didn't and the original poster on Disney Treasures ignored comments from users complaining that the story was an April Fool's joke from this past spring.
Also, perhaps, most hilariously, they both copied and pasted a link that when you click on it sends you to a photo of this man saying, "OMG April Fool!"
So, no, there is no Full House reboot coming down the pipeline.
But regardless of facts, sometimes the internet likes to decide something is happening and just roll with it.