I’m betting that Brett Baier will replace him.
That said; Fox News will not feel quite the same without Britt and I know his team will miss him greatly. That he will still be 'contributing' is good; and will look forward to those contributions. (I miss E.D. Hill and yes, John Gibson too. . .)
Britt of course, is a different kind of 'mainstay'/anchor at Fox. Do wish him the best; just hate the six o'clock goodbye! (Wondering if he will be writing a book. . .sounds like he has one to write and has 'wisdom' to share.)