It completed the journey with a 20-second thruster burn to arrive within 12 miles (19km) of the 1,600ft (500-meter) diameter, diamond-shaped space rock.
The low gravity of smaller objects like asteroids makes it more hard to target missions.
Scientists hope it will reveal more about the early formation of the solar system, as well as how to find precious resources like metals and water in asteroids. As it does, the feeble gravity will allow scientists on Earth to calculate the mass of Bennu, which will be a big clue to its composition.
Japan's Hayabusa mission returned a small sample of an asteroid known as 25143 Itokawa in 2010; a successor craft, Hayabusa-2, arrived at an asteroid called Ryugu past year and is expected to return a sample in 2020. The spacecraft won't land but use a three-metre mechanical arm in 2020 to momentarily touch down and pick up particles.
This celestial body in the future could threaten Earth.
OSIRIS-REx's approach surveys of asteroid Bennu This montage includes images from two full rotation surveys of asteroid Bennu by OSIRIS-REx on 25 and 27 November.More news: Fears growing for backpacker Grace Millane missing in New Zealand
Asked how he was feeling at the moment of arrival, principal investigator Dante Lauretta tweeted, "relieved, proud and anxious to start exploring!"
As the craft approaches Bennu, it sends back stunning imagery to NASA.
Scientists estimate there is a one-in-2,700 chance of the asteroid crashing into Earth 166 years from now. In particular, Bennu is a rare subset of asteroid, called a B-type asteroid, which means scientists suspect there should be organic compounds and wet clays on it.
About the size of an SUV, the spacecraft will shadow the asteroid for a year, before scooping up some gravel for return to Earth in 2023.
There is also the possibility the asteroid sample could be rich in a valuable material that could be extracted for use on earth.More news: Kate and William visit military personnel at RAF base in Cyprus
A NASA mission to an asteroid arrives at its destination today.
Note: OSIRIS-REx is not landing on the asteroid today. The sample will be small-only 60 grams, or 2.1 oz. -but that's enough material to meet the missions goals.
Mission team members want to make sure they nail down Bennu's mass and precise shape before slipping into orbit around the asteroid on December 31.
With Bennu some 76 million miles (122 million kilometers) away, it took seven minutes for word to get from the spacecraft to flight controllers at Lockheed Martin in Littleton, Colorado. Its odometer read 1.2bn miles (2bn km) as of Monday.
From that stage, the spacecraft will begin gradually tightening its orbit around the asteroid, spiraling to within just 6 feet of its surface. In July 2020, after a year and a half of detailed mapping and rehearsals, OSIRIS-REx will briefly push TAGSAM, shaped somewhat like an inverted pie dish, into contact with the surface of Bennu.
OSIRIS-REx - whose name stands for "Origins, Spectral Interpretation, Resource Identification, Security-Regolith Explorer" - won't leave Bennu until March 2021, when the probe will head back toward its home planet.More news: Bug Results In Fallout 76 Users Seeing Other People's Support Tickets
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