Newsmax already paid $27 million and has pledged to pay $40 million over a period of two years.
Mr Carlson did not reveal the details of the new show but criticised the traditional media for reporting “lies” to its audience.
The announcement came a few days after the network agreed to pay $787.5m to settle a defamation lawsuit with Dominion Voting Systems.
“I’d never drop out. It’s not my thing,” Mr Trump said when asked about his possible conviction.
Fox News has been sanctioned by the judge overseeing Dominion Voting Systems’ lawsuit against the network.
Billionaire media mogul Rupert Murdoch, 92, divorced four times, has found love again in the arms of Ann Lesley Smith, a 66-year-old police chaplain, whom he met in September last year.
