The FA board unanimously approved Dyke's nomination, and subject to approval by the FA Council the appointment will be confirmed formally.
Bernstein will step down in the summer after two-and-a-half years in charge, during which he oversaw, amongst other things, the departure of England manager Fabio Capello and the subsequent hiring of Roy Hodgson, as well as the opening of the St George's Park complex.
Dyke, 65, is currently the chairman of Brentford in League One. He told the FA website: "Football has always been a big part of my life whether playing 11-a-side on Sunday mornings or six-a-side on Thursday evenings.
"I was brought up in a household where my father was much more interested in whether or not you had won at football than whether you had passed your exams. In my case that was just as well.
He added: "Obviously as Chairman of The FA it is imperative that I am neutral so that means giving up my current role as Chairman of Brentford which I will miss. However I shall be staying on until the end of the season."