Barker remains as a member of the judging panel and will play a major role in this year's 60th anniversary show.
Barker said: "It has been an honour to present BBC Sports Personality of the Year for the last 19 years and I have loved every minute of it.
"The BBC have asked me to stay but I had made the decision to downsize my commitments a while ago, and I knew that the time would be right after what was always set to be a magical 2012."
She added: "I will still be very much involved with the show though, and am looking forward to the 60th Anniversary celebrations coming up this year.
I also of course look forward to continuing my other presenting work on the BBC."
Director BBC Sport Barbara Slater said: "It is with a sad heart that we announce that Sue is no longer presenting, having been the mainstay of the BBC Sports Personality of the Year for almost two decades.
"This is Sue's decision and one that we all respect. However fans needn't worry, she won't be absent from our screens on the night; bringing some special elements to the show as we look back on what has been another bumper year for UK sport. "
She added: "Sue will also remain very much a key part of our presenting team at BBC Sport, as we prepare for a busy 2014 sporting calendar.
"I would also like to take this opportunity to welcome Gabby Logan to the Sports Personality team for 2013, we're delighted to have her on board."
Barker will work for the broadcaster at Wimbledon and the 2014 Winter Olympics.
The 2013 BBC Sports Personality of the Year ceremony will be broadcast live from the first direct arena in Leeds on Sunday, December 15 on BBC One and BBC One HD.
This year's panel is chaired by Slater.
Also on the panel are BBC head of TV Sport Philip Bernie, executive editor of BBC Sports Personality for the Year Carl Doran, BBC Radio 5 live presenter Mark Pougatch, newspaper sports editors Alison Kervin, Adam Sills and Dominic Hart and former nominees Kelly Holmes, Tanni Grey-Thompson and Michael Vaughan, and chief executive UK Sport Liz Nicholl.
The panel will select the shortlist, and the winner will be decided by public vote on the night.
They will also select the winners of the 'Team of the Year', 'Overseas Personality of the Year' and 'Coach of the Year' awards, and other gongs include the Lifetime Achievement award, the Helen Rollason award, 'Young Sports Personality of the Year' and 'Unsung Hero'.
Sports Personality of the Year awards 2012 - in pictures: