The news of the rocket launch was announced on state TV
There's been widespread international condemnation of the launch by North Korea of a long-range rocket.
The United States called it a "highly provocative act that threatens regional security".
China, Pyongyang's closest ally, expressed regret that North Korea had launched a satellite "in spite of the extensive concerns of the international community".
A UN resolution bans North Korea from conducting ballistic missile tests, reports the BBC.
Secretary-General Ban Ki-moon said the launch was a "clear violation" of that resolution.
The Unha-3 rocket, launched at 09:49 local time (00:49 GMT), appears to have followed its planned trajectory, with stages falling in expected areas.
North Korea says a satellite has been placed in orbit; the US confirmed an object had been put into space.
US National Security Council spokesman Tommy Vietor said: "This action is yet another example of North Korea's pattern of irresponsible behaviour. Given this current threat to regional security, the United States will strengthen and increase our close coordination with allies and partners.
"The international community must work in a concerted fashion to send North Korea a clear message that its violations of UN Security Council resolutions have consequences."
Japan has called for an emergency meeting of the UN Security Council. Reports suggested this could take place shortly.
The launch comes a week ahead of the South Korean presidential election and roughly a year after the death of North Korean leader Kim Jong-il, on 17 December 2011.
The three-stage rocket was launched from a site on North Korea's west coast.
"The launch of the second version of our Kwangmyongsong-3 [Unha-3] satellite from the Sohae Space Centre... on December 12 was successful," state news agency KCNA said. "The satellite has entered the orbit as planned."
The rocket had been scheduled to pass between the Korean peninsula and China, with a second stage coming down off the Philippines.
"The missile was tracked on a southerly azimuth [angle]. Initial indications are that the first stage fell into the Yellow Sea," a North American Aerospace Defence Command (Norad) statement said.
Most media outlets from South Korea, Japan and China reported the rocket launch at least an hour before Pyongyang's state-run news agency KCNA and the national radio station.
Most TV stations and news portals described the timing as "unexpected", with China's Xinhua news agency an exception.
Xinhua published a commentary a few hours after the launch and defended North Korea's "right to conduct peaceful exploration" of outer space.
After reporting the launch, South Korean and Japanese media quoted officials of the two countries who were sharply critical of it.
"The second stage was assessed to fall into the Philippine Sea. Initial indications are that the missile deployed an object that appeared to achieve orbit."
The Japanese government, which put its armed forces on alert ahead of the launch, said the rocket had passed over parts of Okinawa prefecture, south of the Japanese mainland.
South Korean President Lee Myung-bak, meanwhile, called an emergency meeting of his top advisers. His foreign minister said the government strongly condemned the launch.
In China, Foreign Ministry spokesman Hong Lei expressed "regret" at the launch. A commentary from state-run Xinhua news agency called on all parties to remain "cool headed" and engage in "trust-building measures".
North Korea had said two days ago that the launch could be delayed because of a technical problem, extending the window until 29 December.
It is believed to be working on the development of a long-range missile capable of reaching the west coast of the US mainland.
It has not previously successfully launched a three-stage rocket. Its most recent test, in April 2012, ended in failure, when the rocket flew for only a few minutes before exploding and crashing into the sea west of the Korean peninsula.
Officials fear it could be working towards a missile on which a nuclear warhead could be mounted - but it is not thought to have fully developed either the missile or the warheads yet.