Former investment banker Ed Woodward will take on the top executive role at United from July, working with manager Alex Ferguson to hire new players for the 19-times Premier League champions.
Woodward, who joined the club in 2005 after its takeover by the American Glazer family in a controversial £790 million deal, replaces long-serving chief executive Gill who is stepping down after a decade in the role and 16 years at the club.
Woodward will retain the title of executive vice chairman but take on the duties vacated by Gill, 55.
A 40-year-old Briton, Woodward worked with the Glazers on their takeover of the club when he was a banker with JP Morgan and then joined United where he helped to organise the club's successful commercial expansion.
He played a prominent role in United's $2.3 billion flotation on the New York Stock Exchange last August and has recently been hosting conference calls with investors when the club publishes its financial results every three months.
As part of United's reorganisation, commercial director Richard Arnold, who has done a series of sponsorship deals around the world, is promoted to the role of managing director.
United regularly attract crowds of 75,000 to Old Trafford and claim to have more than 650 million followers across the globe - making them one of the world's most popular clubs.
Fans and investors who have bought shares in the club will be keen to see how Woodward gets on with Ferguson, the Scot who has managed United since 1986 and led the club to 12 Premier League titles and two European Champions League triumphs.
Ferguson, 71, said he was sorry that Gill was leaving but welcomed the appointment of Woodward.
"He is a young man with the energy and drive to help keep United at the forefront of the game and to help us maintain our success on the field," he said in a statement.
Woodward's role will involve helping to agree transfer fees and wage packages for new additions to a squad that includes England forward Wayne Rooney and Netherlands striker Robin van Persie.
A vocal section of United supporters accused the Glazers of overloading the club with debt and harming its chances of competing with the top teams in Europe.
After a barren season in 2011-12, the signing of Van Persie from Arsenal last August for £24m has helped to silence the critics.
United lead the Premier League by 12 points and are well placed to reach the last eight of the Champions League after a 1-1 draw with fellow European heavyweights Real Madrid in Spain last week.
Gill, 55, joined United in February 1997 as finance director and has been chief executive since 2003. He will remain a club director.
He has been moving more into the politics of the game, having been appointed vice chairman of the English Football Association last year, and will seek a place on the executive committee of UEFA, in elections scheduled for May.