A crowd of up to 12,000 people will watch the "star-studded" event on Sunday December 14 at the SSE Hydro. It will be shown live on BBC One.
The ceremony offers a review of the sporting year and will feature the Winter Olympics, the World Cup and the Commonwealth Games as well as events like Wimbledon, the Six Nations, the Open Championship and the Ryder Cup.
Last year, Wimbledon champion Andy Murray took home the Sports Personality of the Year (Spoty) trophy, which was presented to him in Miami via video-link by Martina Navratilova.
The tennis star told the BBC he would like to be involved in the show again.
He told the channel: "I might make a few changes to my training.
"I may be going to Australia a little bit earlier next year, so I'll maybe come back for Spoty.
"You don't often get that many great athletes in one space at one time, that's what makes the evening so special.
"To have it in Glasgow, they'll put on a good show and the crowd will love it."
Six-times Olympic gold medallist Sir Chris Hoy, also a former winner, said it was "fantastic news" the event was coming to Glasgow.
He told the BBC: "When you walk into the arena, it's like a sporting event in its own right."
He added: "The Glaswegians will put on a great show, like they will do for the Commonwealth Games, as they are passionate people.
"Hopefully, if I get a ticket, as I won't be nominated any more, it will be fantastic."
Organisers said the event will round off a great year for Glasgow, where the Commonwealth Games take place from July 23 to August 3.
Barbara Slater, the director of BBC Sport, said: "As hosts of this year's Commonwealth Games, it's fitting that Glasgow rounds off what will be a spectacular year of sport by staging BBC Sports Personality of the Year.
"This show will be something very special; marking the successes of those who've excelled in their chosen sport in 2014 and welcoming back those who have made history thanks to their previous achievements.
"Plans are now well under way for this year's Sports Personality. I am already looking forward to it."
Local government and tourism chiefs welcomed the news.
Gordon Matheson, leader of Glasgow City Council and chair of Glasgow City Marketing Bureau, said: "We're delighted that Glasgow has been chosen to host the 2014 BBC Sport Personality of the Year in December, rounding off the most spectacular year in our city's sporting history.
"As one of the top five venues in the world, the SSE Hydro is a fitting location to host the star-studded ceremony and strengthens our city's reputation for delivering world-class events on a major scale.
"As we get ready to host the best-ever Commonwealth Games, the BBC Sports Personality of the Year will give us the opportunity to remember and celebrate again the achievements, in Glasgow, of the world's top athletes."
Sports Personality of the Year was devised by Sir Paul Fox in 1954.
Previous winners have included Jayne Torvill and Christopher Dean, Sir Steve Redgrave, David Beckham, Sir Bradley Wiggins and Dame Kelly Homes.
Mike Cantlay, chairman of VisitScotland, said: "This year promises to be a spectacular summer for sport with the Commonwealth Games in Glasgow and the Ryder Cup at Gleneagles.
"It is therefore only fitting that after a year of action on the pitch, course and track that the annual BBC celebration of our sporting heroes takes place in Scotland.
"Hosting the BBC Sports Personality of the Year is another feather in Glasgow's cap as the city positions itself as a key events destination."
Meanwhile, the best of 80s music will also be entertaining audiences at the venue as Culture Club have announced a Glasgow date as part of their tour.
The band, who are fronted by singer Boy George, will be supported by Alison Moyet when they play the venue on Monday, December 1.
Tickets will go onsale at 9am on Friday, May 23, priced £43.12 - £54.32 (inc admin fee) and will be available from www.thessehydro.com or 0845 395 4000.