Gill has been on the United board since 1997 when he was named finance director, and he has been in his current role since 2003, but he will remain with the club as a director.
Executive vice chairman Ed Woodward will assume Gill's responsibilities when his tenure ends on 30 June.
Gill was appointed vice chairman of the Football Association in October 2012 and has been nominated as a candidate in the upcoming UEFA Executive Committee elections in May 2013.
"It has been the greatest privilege to serve Manchester United for 16 wonderful years - the last 10 of which as its chief executive," Gill said on the club's official website.
"I have worked alongside the finest manager in the history of the game and been part of what I consider to be the best club in the best sport in the world.
"It has been a very hard decision because I love this club and, as the fans' banner says, it is, 'more than a religion'.
"I've experienced some incredible highs, such as the treble in 1999 and the League and Champions League double in 2008, and lows, like losing the title with the last kick of the season last year. But that is what makes this club and this sport so compelling.
"However, I have always been conscious of the fact that, as a member of staff, I was always just a temporary custodian of this marvellous institution.
"I am also of the view that all businesses need to refresh with new management and ideas and after 10 years in charge I believe it is appropriate for someone new to pick up the baton.
"I'm delighted Ed has accepted the role. I have worked with him for more than seven years and in that time he has built up knowledge of football matters, which will hold him in good stead for the future."
A big loss
United boss Sir Alex Ferguson said: "I have been here for over 26 years and for 23 of those years my boss has been one of only two men: Martin Edwards, who brought me to the club, and David Gill. I have enjoyed working with both.
"David has been a magnificent chief executive. Of course, we have had a million arguments, but I have always enjoyed them because I know that David has two great qualities: he is straight and he always puts Manchester United first.
"No disagreement is ever personal with him. He always wants the best for United, whether it's the players, the training ground or the staff.
"Him stepping down is a big loss to me but the fact that he is staying on the board encourages me that the reason for his departure is heartfelt, that he believes it is time for the club to move on.
"If I could have found a way of persuading him to stay I would love to have done that. But he has made his decision and I respect him for it."