The Brighton-based writer made the announcement on her Facebook page on Tuesday.
“I’ve been sacked by the Telegraph – it’s been a lovely five years, and I’ll always be grateful to them for ending my wilderness years,” she wrote.
“However, I’d be lying if I said that I hadn’t often moaned to my husband recently about them always rejecting my edgy column ideas and giving me more pedestrian ones – which I’ve done splendidly anyway.”
“Onwards and upwards!” she added.
Telegraph Media Group has been contacted for comment.
After the Duke and Duchess of Sussex announced the arrival of their second child on Sunday, Ms Burchill tweeted: “What a missed opportunity! They could have called it Georgina Floydina!”
The post was met with a backlash on social media, where it was described as “disgusting racism” and “despicable”. A barrister who tweeting an offensive joke in response to Burchill’s post was suspended from her job on Monday and apologised.
George Floyd’s murder by a white police officer last summer in Minneapolis led to worldwide Black Lives Matter protests.