The rocket took off at around 9am Pyongyang time from the North's west coast, according to South Korea's defense ministry.
In a state TV broadcast, a female North Korean announcer, wearing a traditional dress, said the "epochal" launch, personally ordered by leader Kim Jong-Un, had "successfully put our Earth observation satellite... into orbit".
Japan's NHK broadcaster said that debris from the rocket was believed to have fallen about 155 miles (250km) off the southwest coast of the Korean Peninsula into the East China Sea about 14 minutes after the launch, Sky News reported.
It also showed footage of an object visible in the skies from the southern island of Okinawa that was believed to be the rocket.
Both US Secretary of State John Kerry and Japanese Prime Minister Shinzo Abe condemned the launch as "a violation" of UN Security Council resolutions.
Mr Kerry said it was the second time in just over a month that North Korea has chosen to conduct "a major provocation, threatening not only the security of the Korean Peninsula, but that of the region and the United States as well".
South Korean President Park Geun-Hye urged the UN to "take strong punitive measures quickly".
The US, Japan, and South Korea have requested an emergency meeting of the Security Council to discuss the North's actions and whether to push for more tough sanctions.