The spacecraft is scheduled to arrive at the Texas-sized planetary body on March 6, finishing the last 640,000 kilometres of its journey.
A Delta-II rocket launched Dawn in September 2007 from the Kennedy Space Center at Cape Canaveral in Florida to begin a seven-year trip covering 4.7 billion kilometres.
Dawn has been moving with ion propulsion thrusters, which are commonly used in satellites. This kind of gentle propulsion is created by electrostatically accelerating ions, which are expelled out of the spacecraft's three xenon ion thrusters.
Before heading to Ceres, Dawn travelled four years to reach Vesta, another asteroid or minor planet, in 2011. During its 14 months in orbit, Dawn mapped the surface and discovered a mountain much taller than Everest.
The two planetary bodies are in the same asteroid belt between the orbits of Mars and Jupiter and both orbit the Sun.
Ceres is the largest body in the belt, with an average diameter of 950 kilometres, while Vesta has an average diameter of 525 kilometres.
Astronomers believe Ceres has an icy crust and a cooler interior than Vesta.
NASA says Dawn will use the next couple of months of the approach phase to take the best images of the dwarf planet ever recorded.