The world number one, who had been offered a reported $2 million (£1.27million) to return to the event in which he finished second to Thomas Bjorn two years ago, has decided against the trip as war looms with Iraq.
On Friday defending champion Ernie Els, the world number two, said he would be playing.
But Woods joins a list of golfers who have withdrawn from the tournament - including three former winners in Colin Montgomerie, Seve Ballesteros and Mark James as well as Nick Faldo and Paul Casey.
Woods said he has decided not to travel outside the United States at this time.
"Although I originally intended to play this week I have reluctantly decided to postpone my appearance until next year," he said.
Woods added: "The organisers of the event have been extremely co-operative and supportive and I appreciate their understanding.
The tournament's executive committee chairman Mohamed Ali Alabbar stated: "While we are disappointed with Tiger's decision we are delighted he has immediately confirmed his participation for next year.
Alabbar added: "Those who know the UAE (United Arab Emirates) as a country of peace and harmony will understand that the situation in Dubai is as normal, with all of us working towards the goal of making this year's tournament a huge success.
"And why wouldn't it be a success? We have the defending champion Ernie Els, record prize money, the backing of our valued family of sponsors, the full support of the European tour and many of the biggest names in world golf."
Ireland's Darren Clarke and Lee Westwood will be competing alongside Els, but have pulled out of the following week's Qatar Masters, as have defending champion Adam Scott and a host of others. Padraig Harrington plays in both.
Woods, who has massive security around him wherever he goes and has had a number of death threats made against him during his life, commented earlier in the week: "Any time you go overseas and there's war not too far away, it is a danger."
His management company had kept in constant touch with the American government about the situation, but on the advice they had given he stated: "It keeps changing. They're giving the politically correct answers to our questions, which is pretty much nondescript."
There appeared considerable doubt about Els' participation on Wednesday when he said: "I would love to go it's one of my favourite events, but my only scare is if I get there and it (war with Iraq) kicks off. How do you get out?
"We've spoken to the people over there and they said come, but at the end of last week there was some (British) government advice about not going to Qatar. What's the big difference between Qatar and Dubai?"
But after further talks and watching developments on television he gave the event a massive boost by giving it the go-ahead.
"Ernie Els is a champion in every sense of the word," said Alabbar.
"He is a world superstar and a hugely popular player who has shown himself to be the world's top tournament golfer this year.
"Ernie has a huge fan base in Dubai and I seriously hope and expect that the spectators turn up in their thousands to show their support for Ernie after he has shown his support for Dubai and the Desert Classic."
So far in 2003, Els has played six, won four and been second once. Dubai could have produced the first meeting of him and Woods this season, but that will now be in the Bay Hill Invitational in Florida on March 20-23.