It is the smallest object ever to be orbited by a human-made spacecraft.
After backing away, OSIRIS-REx will direct the robot arm to place the collector inside an aerodynamic sample return capsule. OSIRIS-REx will spend the next 18 months there, surveying the landscape and probing Bennu's chemical makeup before finally selecting what piece of the asteroid it wants to bring back home.
"Relieved, proud, and anxious to start exploring!" tweeted lead scientist Dante Lauretta of the University of Arizona. "To Bennu and back!"
With Bennu more than 80 million miles away, it took seven minutes for word to get from the spacecraft to flight controllers at Lockheed Martin in Littleton, Colo.
The spacecraft design, a 4,650 pound craft when fueled, draws on Mars Reconnaissance Orbiter heritage and was built in their Denver facility.
Bennu is estimated to be just over 1,600ft (500 metres) across.
OSIRIS-REx scientists expect to reveal the results of their early surveys of Bennu next week at the fall meeting of the American Geophysical Union in Washington. NASA scientists think the 484-meter-wide rock was once part of a much larger asteroid, which Space.com suggests was as large as the USA state of CT (which is 110 miles wide and 70 miles long), that was blown apart by some colossal collision a billion years ago.
Scientists hope they will get to examine the contents of an astronomical time capsule, with the carbon-rich material taken from Bennu's surface holding evidence from the beginning of the solar system 4.5bn years ago. "This successful test shows that, when the time comes, TAGSAM is ready to reach out and tag the asteroid".
Space agency NASA estimates its space probe will reach the distant asteroid around 5pm GMT (12pm EST) today.
Soon an image of the asteroid appeared on the mission control screens: a diamond-shaped body with a rough, speckled exterior.
Ryugu's specks should be here by December 2020 but will be far less than Osiris-Rex's promised booty.
Osiris-Rex aims to collect at least 60 grams, or 2 ounces, of dust and gravel.
The spacecraft will use a 3-meter mechanical arm to obtain the samples, as it is not set to actually land on the asteroid.
The collection - parachuting down to Utah - would represent the biggest cosmic haul since the Apollo astronauts hand-delivered moon rocks to Earth in the late 1960s and early 1970s.
The asteroid may provide answers to the origin of our solar system, according to NASA. Japan managed to return some tiny particles in 2010 from its first asteroid mission, also named Hayabusa.
An interplanetary visitor has arrived at asteroid Bennu.
Contact with Bennu will not significantly change its orbit or make it more risky to us, Lauretta stressed. An asteroid like Bennu, which contains frozen water, may have brought water to Earth during an ancient collision - a collision that ultimately may have allowed life to flourish on our humble blue home.
NASA said: "OSIRIS-REx launched in September 2016 and has been slowly approaching Bennu". Its odometer read 1.2bn miles (2bn km) as of Monday.
Over the next year, OSIRIS-REx will survey the asteroid using five scientific instruments on board the spacecraft.
Yet Bennu's small size also makes it possible for OSIRIS-REx to perform a series of carefully choreographed hairpin maneuvers around the asteroid.
That's why NASA has spent $800 million on the Origins, Spectral Interpretation, Resource Identification, Security, Regolith Explorer (OSIRIS-REx) program, launching a spacecraft to the space rock for an up-close-and-personal inspection of Bennu.
The Associated Press contributed to this article.