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.
What started out as a Christmas comedy caper has become quite the seasonal thriller. It’s got everything: cyber-attacks, terror threats and an international incident between America and North Korea, but all of it is a drama Sony Pictures could do without.
The company has been through a lot in the last month, and has now backtracked on its decision to pull the film completely. As yet the big theatres have still not said when, or whether, they might screen the film.
Sony Pictures Entertainment has been hit hard – first by the embarrassment of personal emails being dumped online. But as the seriousness of the cyber-attack unfolded, it also became clear that the personal details of thousands of staff and former-employees had been stolen – opening the door to class-action lawsuits.
Unreleased films leaked online, and then the pulling of a major movie, could cost tens of millions of dollars – let alone the price for the computer network repairs and beefed-up security.
It’s a still-unfolding script to a drama the critics might even slam for being a little too far-fetched.
Earlier, Seth Rogen, who directed and starred in the film, tweeted: “The people have spoken! Freedom has prevailed! Sony didn’t give up!”
Co-star James Franco added: “Victory! The people and the president have spoken!”
Hundreds of independently-owned theatres had signed a petitionexpressing 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.
The Interview features James Franco and Seth Rogen as two journalists granted an audience with Mr Kim. The CIA then enlists the pair to assassinate him.
22 November: Sony computer systems hacked, exposing embarrassing emails and personal details about stars
7 December: North Korea denies accusations that it is behind the cyber-attack, but praises it as a “righteous deed”
16 December: “Guardians of Peace” hacker group threatens 9/11-type attack on cinemas showing film; New York premiere cancelled.
17 December: Leading US cinema groups say they will not screen film; Sony cancels Christmas Day release.
19 December: FBI concludes North Korea orchestrated hack; President Obama calls Sony cancellation “a mistake”
20 December: North Korea proposes joint inquiry with US into hacks, rejected by the US.
22 December: North Korea suffers a severe internet outage.
23 December: Sony bosses say they will now give The Interview a limited Christmas Day release.