Dyke, 65, will replace Bernstein, who has been in the position for two-and-a-half years on Saturday July 13, subject to approval by the FA Council.
Dyke has worked as Director General of the BBC and Managing Director of London Weekend Television, but he has also had a long background in football.
He was a director of Manchester United in the late 1990s and has been non-executive chairman of Brentford since 2006.
Dyke, who will relinquish his role with the Bees at the end of the season, said: "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.
"I still turn out to play six-a-side some Thursday evenings although at my age I seem to spend more time injured than playing.
"I supported my local team Brentford as a kid where my elder brother was a junior, watched York City while at university and followed Manchester United whenever I could.
"I got involved in how the game was run when I was first involved in buying sports rights. I learnt a lot in the years when I was on the board of Manchester United and have seen the other side of the professional game at Brentford."
Dyke, who will also give up his role as chairman of German broadcaster Pro Sieben, 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.
"As I leave I would like to pay tribute to everyone at Brentford, the staff, the players and manager and particularly the fans. I hope their loyalty is rewarded with promotion, it deserves to be.
"I am very excited to take on this role with the FA. At the grass roots seven million people play football every weekend, women's football is booming and the ambition is for it to be the second-biggest team participation sport in England behind only the men's game, we have the best known, most successful league in the world with the Premier League and the Football League is so much stronger than it was eight years or nine ago.
"Having said that I am a big supporter of financial fair play which, in both the Premier League and the Football League, will have a big impact and hopefully bring a degree of financial sanity to the professional game.
"I do see one of the most important tasks for the FA is, over time, to make thoughtful changes which will benefit the England team.
"The FA have made a great start by rebuilding Wembley and developing great facilities at St George's Park but it is essential that the FA finds a way to ensure that more talented young English footballers are given their chance in the professional game at the highest level."