"The Colombian Football Federation (FCF) has presented the letter of intent," FCF president Luis Bedoya said. "We know it's going to be a long, tough road.
The announcement represented an about-turn for the FCF which three years ago joined the federations of the other South American nations in unanimously backing Brazil as the continent's only candidate to stage the competition.
With the event earmarked for South America under FIFA's rotation system, that decision effectively left Brazil to bid unopposed.
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However, the FCF changed its mind after President Alvaro Uribe made a speech in July during which he said he wanted the country to join the race.
Vice-president Francisco Santos said much work needed to be done, pointing out Colombia did not have the stadiums nor infrastructure necessary to host the event.
"We can do it, we can provide the necessary investments and the country has to start thinking about big projects," he told Reuters. "Countries need to have dreams, they need great achievements."
Colombia were awarded the 1986 finals but pulled out because of financial difficulties less than two years before the tournament was staged.
Mexico stepped in and staged the competition which was won by Argentina.
Colombia hosted and won the 2001 Copa America which was initially postponed before going ahead at the last minute amid security fears.
Argentina refused to take part and were replaced by Honduras.
South America has not staged the World Cup since 1978 when Argentina were hosts. Brazil, which announced last week that it had officially confirmed its intention to bid, were hosts in 1950.
FIFA president Sepp Blatter has said world soccer's governing body will look elsewhere if none of the South American bids come up to scratch.
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