The probe is set to "document in exceptional detail the mammoth rocky asteroid Vesta, and then, the even bigger icy dwarf planet Ceres," said the space agency's Web site.
Dawn's 4.8-billion kilometer (3-billion mile) voyage began on Thursday morning.
Scientists are eager to compare the two very different heavenly objects in order to learn more about the creation of the solar system.
"The science returned from Vesta and Ceres could unlock many of the mysteries of the formation of the rocky planets, including Earth," said David Lindstrom, Dawn program scientist at NASA Headquarters, Washington.
The Dawn voyage was cancelled by NASA last year due to budget restrictions and technical issues. However, scientists appealed, and won additional funding to continue the program. Total mission costs are expected to reach around $450 million.
During the course of its eight-year mission, Dawn's three ion propulsion engines will fire cumulatively for about 50,000 hours (over five years) - a record for a spacecraft.
The spacecraft is expected to reach Vesta in 2011 and Ceres in 2015.
