The launch comes eight months after the first test failed to put a dummy satellite into orbit.
South Korea has successfully launched its first domestically-developed space rocket, the country's second attempt after a launch last October failed.
The Korea Satellite Launch Vehicle II, a 200-tonne liquid fuel rocket informally called Nuri, lifted off from the launch site in Goheung at 0700GMT on Tuesday, the government said.
"Nuri has completed its flight according to plan. Engineers are now analysing its flight data, which will take around 30 minutes to complete," said Oh Tae-seok, Seoul's deputy minister of science, technology and innovation.
South Korea's second test launch of its homegrown space rocket comes eight months after the first test failed to put a dummy satellite into orbit.
On Tuesday, it appeared that stage of the launch had worked as planned.
"Nuri separates dummy satellite," South Korea's YTN Television reported minutes after lift-off, adding shortly after that the launch "appears to be a success".
South Korea says it had successfully launched its homegrown space rocket and placed payload into orbit in "giant leap" for country's quest to become advanced space-faring nation pic.twitter.com/6gFUd0YUqm— TRT World Now (@TRTWorldNow) June 21, 2022
In Tuesday's test, in addition to the dummy satellite, Nuri carried a rocket performance verification satellite and four cube satellites developed by four local universities for research purposes.
The three-stage Nuri rocket has been a decade in development at a cost of $1.5 billion (2 trillion won). It weighs 200 tonnes and is 47.2 metres (155 feet) long, fitted with a total of six liquid-fuelled engines.
Asia, China, Japan and India all have advanced space programmes, and the South's nuclear-armed neighbour North Korea was the most recent entrant to the club of countries with their own satellite launch capability.
Ballistic missiles and space rockets use similar technology and Pyongyang put a 300-kilogram (660-pound) satellite into orbit in 2012 in what Washington condemned as a disguised missile test.
Even now, only six nations, not including North Korea, have successfully launched a one-tonne payload on their own rockets.
The launch has made South Korea the seventh nation in the world to have mastered technology to launch a space vehicle that carries more than a one-tonne satellite.
The test looks set to bring South Korea closer to achieving its space ambitions, including a plan to land a probe on the Moon by 2030.
South Korea plans to conduct four more such test launches by 2027.