Cleese told BBC Radio 4's Today programme: “The BBC have not come to me and said: ‘Would you like to have some one-hour shows?’
“And if they did, I would say: ‘Not on your nelly!’ Because I wouldn’t get five minutes into the first show before I’d been cancelled or censored.”
The comedian and actor will co-host with satirical comedian Andrew Doyle, who currently presents weekly show Free Speech Nation on GB News.
Cleese said: "I was approached and I didn't know who they were. I don't know much about modern television because I'd pretty my given up on it. I mean English television.
"People say it's a right wing channel - it's a free speech channel."
He added: "The whole point is, is it free speech or not? And after I start the show, we'll find out."
Cleese said he believed that woke culture was "worse in America" and added, "The way the woke people conduct their campaign is not very honest."
Asked about the line between free speech and promoting factual inaccuracies, Cleese said: “That’s the job, to put the facts out there, and then to have opinions slightly separate and have a proper argument about it, but not to try to avoid a public debate and then try and get yourself through (on) social media.”
Cleese described himself as an "old-fashioned liberal" but said he was no longer aligned to a particular political party in the UK as he found it a "confusing mess".
He said: “After that appalling debate on Brexit, when I thought this country had sunk to the lowest intellectual level I can ever remember, I kind of lost interest.”
He added “I live in hotel rooms. I’m in hotel rooms 10 months of the year, so I’m interested in a lot of political things everywhere. But I don’t think that this country is in a good state at the moment.
“In fact, I think the last three Tory administrations have been progressively more and more disastrous.”
Last year Cleese spoke out against GB News on social media, implying the broadcaster was controlled by Russia.
He said: "One if its original founders seems to have made some money in Russia but it's no more than that, so I'm satisfied at the moment."
Cleese, who has been a Twitter user since 2007 and has over 5.7 million followers, joined Instagram at the beginning of April 2020, admitting he was feeling bored during lockdown.
Cleese lived in Los Angeles during the 1980s and 90s before returning to the UK, and spoke in 2018 of plans to relocate to the Caribbean island of Nevis.
In 2019 he said London had disappointed him as it was "no longer an English city".
Watch: John Cleese thinks the UK is a mess