Critics of the rocket program say it is being used to test technology for a long-range missile.
The U.S. Strategic Command said it had detected a missile entering space, and South Korea's military said the rocket had put an object into orbit.
North Korea said the launch of the satellite Kwangmyongsong-4, named after late leader Kim Jong Il, was a "complete success" and it was making a polar orbit of Earth every 94 minutes. The launch order was given by his son, leader Kim Jong Un, who is believed to be 33 years old.
North Korea's state news agency carried a still picture of a white rocket, which closely resembled a previously launched rocket, lifting off. Another showed Kim surrounded by cheering military officials at what appeared to be a command center.
Isolated North Korea's last long-range rocket launch, in 2012, put what it called a communications satellite into orbit, but no signal has ever been detected from it.
"If it can communicate with the Kwangmyongsong-4, North Korea will learn about operating a satellite in space," said David Wright, co-director and senior scientist at the Global Security Program of the Union of Concerned Scientists.
"Even if not, it gained experience with launching and learned more about the reliability of its rocket systems."
The rocket lifted off at around 9:30 a.m. Seoul time (0030 GMT) on a southward trajectory, as planned. Japan's Fuji Television Network showed a streak of light heading into the sky, taken from a camera at China's border with North Korea.
North Korea had notified United Nations agencies that it planned to launch a rocket carrying an Earth observation satellite, triggering opposition from governments that see it as a long-range missile test.
The U.N. Security Council condemned the launch in an emergency meeting on Sunday, and vowed to take "significant measures" in response to Pyongyang's violations of U.N. resolutions, Venezuela's U.N. ambassador said.
U.S. Ambassador Samantha Power told reporters: "We will ensure that the Security Council imposes serious consequences. DPRK's (North Korea) latest transgressions require our response to be even firmer."
The United States and China began discussing a U.N. sanctions resolution after Pyongyang's Jan. 6 atomic test.
North Korea had initially given a Feb. 8-25 time frame for the launch but on Saturday changed that to Feb. 7-14, apparently taking advantage of clear weather on Sunday.
North Korea's National Aerospace Development Administration called the launch "an epochal event in developing the country's science, technology, economy and defense capability by legitimately exercising the right to use space for independent and peaceful purposes".
The launch and the nuclear test are seen as efforts by the North's young leader to bolster his domestic legitimacy ahead of a ruling party congress in May, the first since 1980.
North Korea's embassy in Moscow said in a statement the country would continue to launch rockets carrying satellites, according to Russia's Interfax news agency.
NEW MISSILE DEFENSE?
South Korea and the United States said that if the advanced missile defense system called Terminal High Altitude Area Defence (THAAD) was deployed to South Korea, it would be focused only on North Korea.
Source: reuters On photo: A passenger walks past a TV screen broadcasting a news report on North Korea's long range rocket launch at a railway station in Seoul, South Korea, February 7, 2016 (Reuters).