He had earlier criticised Sony for pulling the film following a cyber-attack and threats against cinemas.
The US has accused North Korea of being behind the cyber-attack.
The film is expected to show in 200 mostly independent and art-house cinemas on Thursday. Hackers have threatened fresh attacks.
Mr Obama had called Sony?s earlier decision to cancel the film?s release a ?mistake?.
His spokesman, Eric Schultz, said in a statement that the president applauded the change of mind.
?As the president made clear, we are a country that believes in free speech, and the right of artistic expression,? the statement said.
?The decision made by Sony and participating theatres allows people to make their own choices about the film, and we welcome that outcome.?
North Korea has denied that it was behind the cyber-attack on Sony. But it praised the attack and had long condemned The Interview, which depicts a fictional plot to assassinate North Korean leader Kim Jong-un.
The Interview was originally due to be released on up to 3,000 screens on Christmas Day.
Sony Entertainment CEO Michael Lynton said his company had ?never given up? on a release, and was continuing efforts to have the film shown more widely.
Earlier, Seth Rogen, who directed and starred in the film, tweeted: ?The people have spoken! Freedom has prevailed! Sony didn?t give up!?
Hundreds of independently-owned theatres had signed a petition expressing support for the film and its screening.
Criticism of Sony had also come from Congress and from Hollywood, with some calling the initial decision an attack on freedom of expression.
In recent days North Korea has suffered severe internet outages, though it is not clear what caused the disruption. President Obama had previously vowed to respond to the cyber-attack against Sony, but US officials declined to comment on whether the US was responsible.