The Parker Solar Probe blasted off on its unprecedented $1.5 billion mission on Sunday morning.
For the second day in a row, thousands of spectators packed the launch site at Cape Canaveral, Florida, in the middle of the night.
Among the crowds was 91-year-old astrophysicist Eugene Parker, after whom the spacecraft is named. He proposed the existence of the solar wind 60 years ago.
The successful launch came after Saturday morning's attempt was foiled by last-minute technical trouble.
The Delta IV Heavy rocket thundered into night sky, thrilling onlookers for miles around.
NASA needed the 23-story United Launch Alliance rocket to get the car-sized Parker probe racing towards the Sun at 430,000 miles an hour, faster than any spacecraft in history.
It eventually will get within 3.8 million miles of the star's surface, staying comfortably cool despite the extreme heat and radiation, and allowing scientists to explore in a way never before possible.
Protected by a revolutionary new carbon heat shield known as the Thermal Protection System (TPS), the spacecraft will zip past Venus in October. That will set up the first solar encounter in November.
Temperatures are expected to reach up to 1,400C, but NASA says the TPS has been tested to withstand up to 1,650C temperatures and "can handle any heat the Sun can send its way".
From Earth, it is 93 million miles to the Sun and the Parker probe will be within 4 per cent of that distance, seven times closer than previous spacecraft.
Altogether, the Parker probe will make 24 close approaches to the Sun on the seven-year mission.
The mission is to help scientists unlock the mysteries of the star's atmosphere and answer questions like why its corona, the outermost layer of the solar atmosphere, is hotter than its surface.
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The corona is 300 times hotter than the surface of the Sun, a phenomenon that NASA says is in "defiance of all logic" because "its atmosphere gets much, much hotter the farther it stretches from the Sun's blazing surface".
