The 208-foot (63-meter) tall rocket, built and operated by privately owned Space Exploration Technologies, bolted off its seaside launch pad at 3:25 p.m. EDT/1925 GMT, darting through overcast skies as it headed toward orbit.
The Dragon cargo ship, which is loaded with about 5,000 pounds (2,268 kg) of equipment, science experiments and supplies, is due to reach the station on Sunday.
The station, a $100 billion research laboratory owned by 15 nations, flies about 260 miles (418 km) above Earth.
The cargo run is the third by Space Exploration Technologies, or SpaceX as the company is known, under a 12-flight, $1.6 billion contract with NASA. The U.S. space agency relies on SpaceX and a second firm, Orbital Sciences Corp. to fly supplies to the orbital outpost since the space shuttles were retired in 2011.
NASA also is planning turn over crew transport from Russia to private industry by 2017.
SpaceX had planned to fly last month, but delayed the mission to review a potential contamination issue with its rocket. The issue was resolved, but then an Air Force radar system, needed to track the vehicle during flight, was damaged, sidelining all launches from Cape Canaveral for two weeks.
Another launch attempt on Monday was called off after a valve leak was found in a part of the system that separates the Falcon 9's first and second stages. The rocket was removed from the launch pad and repaired.
On Friday, the only issue was the weather, but the rain and thunderstorms that clobbered Central Florida on Friday cleared in time for the Falcon 9 to lift off at the precise moment when Earth's rotation aligned its launch pad into the plane of the space station's orbit.
"Mother Nature is providing a window of opportunity today," NASA mission commentator Michael Curie said shortly before launch.
SpaceX planned to use Friday's launch to test technology it has been developing to recover and reuse its rockets.
The Falcon 9's first stage holds extra fuel and four landing legs. After it separated from the upper stage and Dragon capsule, the rocket was expected to reignite its engines to slow its descent and position itself for a vertical touchdown on the ocean before toppling over on its side.
"This is a really difficult maneuver," SpaceX Vice President Hans Koenigsmann told reporters during a prelaunch press conference.
Overall, the company considers the test has less than a 40 percent chance of success. There was no immediate word on whether the test was successful.
Eventually, SpaceX hopes to fly its Falcon rockets back to land for refurbishment and reuse.