Obama had made the promise to shut the US prison while on the campaign trail, but his comments on Sunday were the first confirmation of his intentions since the November 4 election.
He did not, however, elaborate on where the Guantanamo detainees would be sent or whether they would be put on trial, or released.
Obama's comments also came as the US revealed that it had held a dozen juveniles at Guantanamo, four more than it had reported to the United Nations in May.
|The US still holds about 250 detainees
at the Guantanamo camp [EPA]
On Sunday Commander Jeffrey Gordon, a Pentagon spokesman, said the government had revised the figure in the report to the UN committee on child rights.
"As we noted to the committee, it remains uncertain the exact age of many of the juveniles held at Guantanamo, as most of them did not know their own date of birth or even the year in which they were born," he added.
The admission came after a study released by the Centre for the Study of Human Rights in the Americas last week said the US has held at least a dozen juveniles at Guantanamo, including a Saudi who committed suicide in 2006.
"The information I got was from their own sources, so they didn't have to look beyond their own sources to figure this out," said Almerindo Ojeda, director of the centre at the University of California in Davis.
The study said eight of the juveniles have been released.
About 250 prisoners are still being held at the US naval camp in Cuba on suspicion of terrorism or links to al-Qaeda or the Taliban.
Rights groups have urged Obama to move swiftly on shutting the prison, widely condemned by the international community, once he moves into the White House in January.
Obama said his number one priority was to repair the stricken US economy by pushing for a stimulus package, adding that it would be a "disaster" for the government to just let the country's automotive industry collapse.
The government will have to do "whatever it takes" to revive the US economy and to "avoid a deepening recession", he said.
But he told CBS that as soon as he takes office on January 20, he and his security advisers will "start executing a plan that draws down our troops" from Iraq.
And he added that "it is a top priority for us to stamp out al-Qaeda once and for all" and that killing or capturing the group's mastermind Osama bin Laden was "critical" to US security.