Simon Coell's Syco production company is on course to reveal a three year extension to the current contract with ITV for both shows later this week.
The Sunday People newspaper reports that an official announcement could be made at the Edinburgh TV Festival if things go to plan.
The deal comes after six months of talks and is said to involve Simon taking a personal pay cut from his £25 million fee as a judge and producer on the shows.
"Finally after months of intense talks, all sides are happy and the new deal has been agreed," a source explained. "It just has to be signed off.
“A formal announcement will be made shortly – hopefully in Edinburgh – as no one is expecting any major hitches. It’s planned to be the big show-stopping announcement of the festival."
Speaking at the start of August, Simon had told the Daily Mirror newspaper that a new deal with ITV was "pretty much there."
And he revealed: “We got calls from everyone, in terms of TV channels. I felt secure about it.
“Sometimes I go back and look at figures from four, five years ago.
“Of course we were doing more numbers but in those days the soaps were doing 14 million too.”
The new contract would secure The X Factor and Britain's Got Talent for a further three more series each, up to the end of 2019.
For now, the upcoming thirteenth series of The X Factor begins this Saturday night on ITV.