American Jessica Buchanan, 42, and Poul Hagen, 60, of Denmark, aid workers for the Danish Refugee Council's demining group, were kidnapped in October in Galkaiyo, Somalia, while visiting a local project site, the council said.
U.S. officials said the pair were safely rescued Tuesday after a shootout with Somali pirates.
President Obama authorized the operation.
"As commander-in-chief, I could not be prouder of the troops who carried out this mission, and the dedicated professionals who supported their efforts," the president said Wednesday in a statement. "Jessica Buchanan was selflessly serving her fellow human beings when she was taken hostage by criminals and pirates who showed no regard for her health and well-being."
Obama said he told Buchanan's father Tuesday night that "all Americans have Jessica in our thoughts and prayers, and give thanks that she will soon be reunited with her family."
"The United States will not tolerate the abduction of our people, and will spare no effort to secure the safety of our citizens and to bring their captors to justice. This is yet another message to the world that the United States of America will stand strongly against any threats to our people," Obama said.