NATO Secretary-General Anders Fogh Rasmussen said the coalition's "goal is to protect civilians and civilian-populated areas under threat of attack” from Col. Moammar Gadhafi.
The move comes days after the alliance assumed command of a sea-based arms embargo and a no-fly zone.
"We have directed NATO's top operational commander to begin executing this operation with immediate effect," the secretary-general said.
U.S. European Command chief Adm. James Stavridis is NATO's top general.
Last Thursday, NATO took control of the no-fly zone, but not the "protecting civilians" aspect of the mission.
That omission raised eyebrows in Washington, but Obama administration and Pentagon officials — who have been eager to put a non-U.S. face on the campaign — said they expected the alliance would soon command all three parts of the mission.
President Obama is sure to tout the handover in an address to the nation scheduled for Monday evening.