The move is expected to be among a series of symbolic changes he will push through quickly to stamp his mark on the presidency.
He is also expected to reverse several controversial executive Bush decisions within days of taking office next week.
Mr Obama has committed to closing the US military prison at Guantanamo Bay and will formally ban all interrogative techniques that could be described as torture, such as waterboarding.
It is expected that he will also reverse Mr Bush's orders restricting the distribution of funds for stem cell research and to overseas groups that offer abortion counselling.
The change of policy on homosexuality will allow gays to serve openly in all branches of the armed forces.
Though a timeline was not put on the reversal of the policy, Robert Gibbs, who becomes Mr Obama's press secretary next week, was unequivocal that it would happen.
When questioned about whether the policy would change on the Obama transition website, he wrote: "You don't hear politicians give a one-word answer much. But it's 'Yes'."
Mr Obama opposed the policy during the campaign, but since his election has made statements that gay pressure groups interpreted as lukewarm commitments.
The issue became a distraction in the early days of Bill Clinton's presidency. He tried to push through reform that would have allowed gays and lesbians to serve openly but had to compromise with the "don't ask, don't tell" solution, which has been maintained by the Bush administration.
Although introduced before he came to power, Mr Bush's refusal to change the "don't ask, don't tell" policy angered many in America.
There is now however much wider public support for removing any restrictions on male and female gay personnel. Colin Powell, the former chairman of the Joint Chiefs of Staff, is among influential figures who have called for the policy to be re-evaluated.
During his campaign Mr Obama often spoke out against what he called Bush's abuse of executive authority.
"I was a constitutional law professor, which means unlike the current president, I actually respect the Constitution," he said in 2007.
Russ Feingold, the Democratic Senator for Wisconsin, a strong critic of Mr Bush’s accumulation of executive power, said he had been informed by Mr Obama’s transition staff the records of past presidents might also be made more available.
He said the incoming president would support a bill he is proposing to make public some opinions from the Justice Department’s Office of Legal Counsel, which issued some of the most controversial extensions of presidential power in the Bush era.
