Obama, in a statement issued by the White House, said the raid was "yet another message to the world that the United States of America will stand strongly against any threats to our people."
Reports said the raid overnight on January 24-25 involved U.S. forces flying in on helicopters and engaging in a gun battle with the pirates, killing up to nine of them.
The hostages -- named as Jessica Buchanan, an American woman, and Poul Hagen Thisted, a Danish man -- were rescued unharmed.
Danish Prime Minister Helle Thorning-Schmidt has also welcomed their freedom.
compiled from agency reports