State television showed huge crowds cheering to mark the launch, which has been condemned by many nations as a banned test of missile technology.
South Korea, meanwhile, says its navy has retrieved debris from the rocket and will study it.
The first stage of the rocket fell west of the Korean peninsula. South Korea’s navy located it shortly afterwards.
It was North Korea’s first successful use of a three-stage rocket to put a satellite into orbit. North Korea said on Friday that more launches would go ahead.
The UN Security Council has condemned the launch, calling it a missile test that violated two UN resolutions banning Pyongyang from such activities passed after its nuclear tests in 2006 and 2009.
The US, South Korea and Japan – who believe North Korea is working to develop long-range missiles capable of carrying nuclear warheads – want action such as the strengthening of sanctions.
But China – North Korea’s main ally – says any UN response should be “conducive to peace” and avoid escalating tensions.
In Pyongyang, state television showed pictures of North Korean leader Kim Jong-un in the control room for the launch, and another of him celebrating with members of the military after it successfully went up.
It also broadcast images of ranks of North Koreans massed in central Pyongyang on Friday to listen to congratulatory speeches.
Kim Ki-nam, party secretary of the Workers’ Party of Korea, told crowds in Kim Il-sung Square that the satellite was “necessary for the building of our national economy”.
“This is an international trend and the justified independent right of our people,” he said.
“Any hostile forces cannot cling to the insistence that our satellite launch is a ballistic missile launch anymore.”
Ro Gwang-chol, vice-chief of the general staff of the army, said that every soldier in the North celebrated the moment and “have been full of delight and strong emotions”.
There was also much praise for the leader.
“This was achieved thanks to the Great Marshall Kim Jong-un’s endless loyalty, bravery and wisdom,” said Jang Chol, president of the State Academy of Sciences.
The rocket was launched from the North Korean coast early on Wednesday. South Korea says a fuel container was found where the first stage of the rocket separated.
“The Navy’s Deep Submergence Rescue Vehicle retrieved the debris of the rocket’s first stage at 00:26 and was delivering it to the Second Command Fleet in Pyeongtaek,” Yonhap news agency quoted a defence ministry official as saying.
It would be “useful material for analysis”, another ministry spokesman said.
On Friday a statement from North Korea’s KCNA news agency said Kim Jong-un had called for more such launches.
North Korea “showed at home and abroad the unshakable stand… to exercise the country’s legitimate right to use space for peaceful purposes”, the KCNA statement quoted him as saying.
The US, meanwhile, said it was holding talks with key players on how to respond to the launch.
“We are working with both our six party partners and with our UN Security Council partners – China is in both of those categories – on a clear and credible response to what the North Koreans have done,” State Department spokeswoman Victoria Nuland said.
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