The cargo rocket lifted off about 8:30 p.m. EDT and reached orbit about 10 minutes later.
"Solar arrays deployed successfully. Dragon on its way to the International Space Station!!" SpaceX staff posted on the private firm's website once Earth orbit was achieved.
About 1,000 SpaceX employees watched the launch from company headquarters in Hawthorne, Calif.
The space shot is the first of 12 cargo missions to the International Space Station, company officials said.
The rocket is carrying a capsule packed with 1,000 pounds of food, water and supplies bound for the space station.
SpaceX performed a successful demonstration mission in May, showing NASA it could do the job -- and securing the $1.6 billion contract.
SpaceX secured a $440 million contract from NASA in August to develop a capsule to carry astronauts.
Company officials said the upcoming cargo missions will provide SpaceX with necessary flight experience for accomplishing that goal by 2015.