The spacecraft was approximately 61,000 kilometres from Ceres when it was captured by the dwarf planet's gravity, NASA said.
Mission controllers at NASA's Jet Propulsion Laboratory (JPL) in Pasadena, California received a signal from the spacecraft that Dawn was healthy and thrusting with its ion engine, the indicator Dawn had entered orbit as planned.
"Since its discovery in 1801, Ceres was known as a planet, then an asteroid and later a dwarf planet," said Marc Rayman, Dawn chief engineer and mission director at JPL.
In addition to being the first spacecraft to visit a dwarf planet, Dawn also has the distinction of being the first mission to orbit two extraterrestrial targets.
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From 2011 to 2012, the spacecraft explored the giant asteroid Vesta, delivering new insights and thousands of images from that distant world, NASA said.
Ceres and Vesta are the two most massive residents of our solar system's main asteroid belt between Mars and Jupiter.
The most recent images received from the spacecraft, taken on March 1 show Ceres as a crescent, mostly in shadow because the spacecraft's trajectory put it on a side of Ceres that faces away from the Sun until mid-April.
"We feel exhilarated," said Chris Russell, principal investigator of the Dawn mission at the University of California, Los Angeles (UCLA).
"We have much to do over the next year and a half, but we are now on station with ample reserves, and a robust plan to obtain our science objectives," said Russell.