The rocket, which was carrying a satellite worth roughly $500m (£393.7m) built by Lockheed Martin, blasted off from Florida just before 2pm GMT.
Delayed several times due to technical issues with sensors and stormy weather, the 229-foot-tall rocket lifted off at 8:51 a.m. ET, climbing straight away from launch complex 40 at the Cape Canaveral Air Force Station, reported CBS News.
SpaceX sued the U.S. Flying corps in 2014 over the military's honor of a multibillion-dollar, non-contend contract for 36 rocket dispatches to United Launch Alliance, an organization of Boeing and Lockheed.
This next-generation Global Positioning System satellite is three times more accurate than previous versions and eight times better at anti-jamming, Heather Wilson, secretary of the Air Force says.
According to Eschenfelder, the next GPS III satellite is set to launch in mid-2019 and additional satellites will be tested at Lockheed's processing facility in Colorado.
"In the coming days, GPS III SV01 will use its liquid apogee engines to climb into its operational orbit about 12,550 miles above the earth". Satellite control and operations are expected to shift to the Air Force's current Operational Control Segment when GPS III Contingency Operations upgrades are fully implemented later this year.
Later on Sunday, Lockheed Martin, who built the satellite, confirmed the GPS III space vehicle had begun receiving and responding to commands.
The launch of the GPS III SV01 satellite, nicknamed Vespucci in honor of Italian explorer Amerigo Vespucci, had originally been scheduled for 6:11 a.m. California time Tuesday.
Mr. Caldwell added: "By this time next year, we expect to also have a second GPS III on orbit and users should be receiving signals from this first satellite".
SpaceX has completed 21 launches in this year, which is more than the 18 launches last year, in what's been a banner year for the company.