A state TV announcer said that North Korea had successfully placed a satellite in orbit.
It appears the rocket was fired from a base in the north-west and passed over Japan's southern Okinawa islands.
The launch was condemned by Japan, South Korea and the US, who have requested an emergency meeting of the UN Security Council later on Sunday.
The North insists its space programme is purely scientific in nature, but the US, South Korea and even ally China say the rocket launches are aimed at developing an inter-continental ballistic missile capable of striking the US.
North Korea has already provoked international criticism this year with a fourth nuclear bomb test on 6 January.
South Korean analysts had speculated that the North might carry out the launch ahead of 16 February, the birthday of the late North Korean dictator Kim Jong Il.
Japanese Prime Minister Shinzo Abe called the launch "absolutely unacceptable," saying it was a "clear violation" of UN Security Council resolutions.
UN Security Council resolutions ban the state from carrying out any nuclear or ballistic missile tests.
US National Security Adviser Susan Rice said North Korea's use of ballistic missile technology was "yet another destabilizing and provocative action".
"North Korea's missile and nuclear weapons programs represent serious threats to our interests - including the security of some of our closest allies," she said in a statement.
Contenders for the Republican ticket in the US presidential election this year were asked for their reaction during a debate in New Hampshire.
Donald Trump said he would work with China to resolve the North Korea nuclear issue: "I would get on with China. Let China solve that problem. They can do it quickly and surgically. That's what we should do with North Korea."
For his part, Chris Christie said of the North Korean government: "All these people understand is toughness and strength."
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North Korea has fired a long-range rocket, which critics say is a test of banned missile technology.