The 46-year-old (pictured, centre), who holed the winning putt in the 2002 match at The Belfry, edged former skipper Colin Montgomerie in a vote taken by the 15-man committee in Abu Dhabi.
Committee chairman Thomas Bjorn said five names were discussed, McGinley, 2010 captain Colin Montgomerie, Paul Lawrie, Miguel Angel Jimenez and Sandy Lyle.
"This is a position I'm really thrilled to be in. It's also a very humbling experience and I can't wait to get into the role of captain and to working with the players," a misty-eyed McGinley said.
"I'm just delighted it's happened and that the cards fell right for me. I think it's very important to have a captain that is still involved regularly as a player on the tour and that's what I plan on doing for the next 18 months until the match."
McGinley replaced Spain's Jose Maria Olazabal, the inspiration behind Europe's remarkable comeback victory in Illinois in September.
He thanked players like world number one Rory McIlroy, third-ranked Luke Donald and last year's Ryder Cup hero Ian Poulter for their public support in the lead-up to the captaincy vote for the 2014 match at Gleneagles, Scotland.
"Paul McGinley 2014 European Ryder Cup captain!!!," McIlroy said on his Twitter account. "Couldn't be happier for him... roll on Gleneagles."
McIlroy was standing up at the back of the room as McGinley made his acceptance speech.
"I'm very fortunate Rory, Ian and Graeme McDowell played under me as a Seve Trophy captain," said the Irishman.
"If there is a good structure on the tour, it is with the Seve Trophy and with the legacy of that tournament.
"Seve was a guy I knew very well. I played under Monty, Jose Maria and Seve in team events so I've been fortunate with the experience I've gained under those captains.
"I have a real passion for team golf and I love it. I love everything that goes with team golf."
McGinley has twice been a Ryder Cup vice-captain, to Montgomerie in Wales in 2010 and to Olazabal two years later.
He served his apprenticeship as a skipper when he led Britain and Ireland to victory over Continental Europe in the Seve Trophy team event in 2009 and 2011.
McGinley played in three Ryder Cups, from 2002-06, and was triumphant each time.
A winner of four European Tour titles, his best campaign was in 2005 when he finished runner-up three times before lifting the season-ending Volvo Masters crown.
In recent times, Europe have taken the view that the Ryder Cup captain should serve for one match only, an approach that was always likely to give McGinley an advantage over chief rival Montgomerie.
"We discussed all the candidates thoroughly but the committee was 100 percent behind this captain," Bjorn said. "It was clear in the meeting room very early which way we wanted to go.
"We listened to the players and we made the right decision. As a captain I think he will bring this tour even more closely together - he's one of us."
McGinley will be up against eight-times major winner Tom Watson who skippers the U.S. in 2014.
"I congratulate Paul McGinley upon his selection as the next European Ryder Cup captain and anticipate his passion and love of the event will transfer to being an outstanding leader of his team," Watson said in a statement.
"Paul is an outstanding representative of European golf. I look forward to sharing the stage with him as we make our journey to Scotland."