United confirmed in a statement released on their official website on Wednesday morning that Gill is to leave his post on June 30, with his duties being taken on by executive vice chairman Ed Woodward.
Gill, who joined the Red Devils as their finance director in February 1997 and assumed the role of chief executive in September 2003, is to remain as a club director.
As part of the statement, Sir Alex Ferguson said: "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, (and) 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."
Speaking about his decision, Gill stressed his belief that "all businesses need to refresh themselves with new management and ideas".
The 55-year-old - who was appointed as the vice chairman of the Football Association last October and is their nominee for the UEFA Executive Committee elections in May - said: "It has been the greatest privilege to serve Manchester United for 16 wonderful years - the last 10 of which as its chief executive.
"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'.
"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 themselves 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 am looking forward to continuing my involvement on the club board. And I hope to be able to make a contribution to the game on a wider national and European level."
Woodward, who has been with United since 2005, described it as a "great honour" to be taking on his new responsibilities.
He added: "I am particularly humbled to have the chance to work alongside the greatest manager in the history of the game.
"Alex's experience and track record are incomparable and I look forward to having the opportunity to support him in shaping his squad in the future and maintaining the club's position at the pinnacle of the sport.
"I'd like to thank David for his help and guidance over recent years, which has helped to develop and hone my experience at the highest level of club football."
Gill has also been commended by United co-chairman Joel Glazer.
"David has played a significant role in the success of Manchester United in his 10 years as chief executive and he can take great satisfaction in all that has been achieved on his watch, both on and off the field," Glazer said.
"I am very pleased he has agreed to remain on the board, so that his experience and counsel is not lost to us.
"I hope that the decision he has made will be to the benefit of the game in Europe as a whole, as he seeks election to UEFA's Executive Committee."
During Gill's tenure as chief executive, United have won four Premier League titles, one FA Cup, three League Cups and the 2008 Champions League.
@Dactyl....the familiar counter story. What you aren't telling us is that the alternative is we just have one, maybe two super clubs spending what they like, hoovering up the best players and killing competition. City's owners have deterred many investors from Prem clubs because whats the point if you can't spend a billion to 'catch up'? City have stolen Evertons place in the CL, why should they suffer because they tried to do it properly? What about the fans with self respect that don't want to see their club transformed and turn into a hobby or advertising project? Blackburn fans, portsmouth fans, Rangers fans, even chelsea fans don't like the way their club is run. You might not like this new ruling, but its certainly for the best.....and when the oil runs out, you'll be grateful.- fishcake