Media playback is not supported on this device
The names will be announced during the One Show on BBC One between 19:00 and 19:30 GMT.
A capacity crowd of about 12,000 will attend the show at the First Direct Arena in Leeds on Sunday, 15 December.
The programme will follow on from last year's awards where Sir Bradley Wiggins was crowned 2012 Sports Personality.
Full roll of honour
After Tuesday's announcement, there will be details of all the contenders and arrangements for public voting on the night at www.bbc.co.uk/sportspersonality.
Tour de France winner and Olympic road cycling champion Wiggins was the latest to join an illustrious roll of honour last year when he received the coveted trophy from the Duchess of Cambridge and former England football captain David Beckham, watched on television by more than 15m people.
Presenter Gary Lineker said: "It's going to be tough to follow last year, the most unbelievable sporting year in living memory, but the fact that it is the 60th anniversary, the fact that it is coming to Leeds, means it's still going to be a huge show."
Director of BBC Sport Barbara Slater added: "We're thrilled Leeds is to host BBC Sports Personality of the Year 2013. The sporting heritage of the city is outstanding and the new arena will be a great venue from which to celebrate the very best of sport."
Devised by Sir Paul Fox in 1954, the first Sports Personality of the Year was held at the Savoy Hotel in London, where it was presented by Peter Dimmock. World record-breaking 5,000m runner Sir Christopher Chataway beat four minute-mile hero Sir Roger Bannister to the award that year as the public voted for the first winner.
The trophy has since been won by many of the greats of British sport, including Bobby Moore, Princess Anne, Lord Coe, Daley Thompson, Jayne Torvill and Christopher Dean, Sir Steve Redgrave, David Beckham, Dame Kelly Homes, Andrew Flintoff, Sir Chris Hoy and many more.
Media playback is not supported on this device
The show went on the road in 2006, taking in Birmingham, Liverpool, Sheffield, Manchester and London. To date, more than 55,000 people have enjoyed spending a spectacular evening with the stars of the sporting year.
Lineker added: "Taking the show out on the road has worked really well. It has proven to be hugely popular. You get thousands of people who can come along and enjoy the live show and it just becomes more of an event.
"When you get the people there who really want to be there - the supporters, the sports fans - it just adds to the atmosphere and I'm sure it will be the same in Leeds."
Most tickets for the event have been sold, although a limited number will be made available later in November.
A shortlist of 10 contenders will be named on Tuesday for next month's 60th BBC Sports Personality of the Year award.