The FA board has unanimously approved the nomination of Dyke, 65, to succeed David Bernstein when he leaves the post in July.
The appointment is subject to the approval of the FA council.
The FA said in a statement: "The Football Association Board has today unanimously approved the nomination for Greg Dyke to be appointed independent FA chairman.
"Dyke, 65, will take over as chairman from David Bernstein when he leaves the post after two-and-a-half years in July - subject to approval by the FA council. The appointment will take effect from Saturday, July 13.
"This follows a recruitment process led by FA independent director Roger Devlin (chairman of the nominations committee) with fellow board members Roger Burden and Keith Lamb.
"In a high-profile broadcasting industry career, Dyke has worked as director general of the BBC and managing director of London Weekend Television.
"Dyke has had a long background in football. He was a director of Manchester United in the late nineties and since 2006 he has been non-executive chairman of Brentford Football Club, the team he supported as a boy. He will relinquish this role at the end of the season to take up his new post at the FA."
Dyke added: "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 as chairman of ITV Sport in the late eighties and later at the BBC. 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 as well as relinquishing his duties at Brentford 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."
In October, the FA council voted not to change a rule which forced Bernstein to retire at the age of 70, a decision which was heavily criticised by sports minister Hugh Robertson.
Reacting to the approval of Dyke as his successor, the outgoing chairman said: "I would like to congratulate Greg Dyke on his nomination to succeed me in July as FA chairman. I wish him every success in this stimulating but demanding role.
"I will ensure that the handover is dealt with efficiently to help in maintaining the stability that has been achieved by The FA since 2010."
Chairman of the nominations committee Roger Devlin said: "We have every confidence we have got the right appointment in Greg Dyke.
"He has an outstanding understanding of football, strong relationships across the industry and Government, while retaining a great empathy for the game.
"I am confident that Greg will be a successful chairman, who will lead the FA from the front and be respected by the football community.
"We have an excellent staff at the FA and I know that Greg is looking forward to working with them."