The Falcon 9 rocket lifted off at 4:10 p.m. EDT from Cape Canaveral Air Force Station Launch Complex 40 into a partly cloudy sky as temperatures reached the mid-90s.
The first-stage booster, which likely will be reused, successfully landed on a SpaceX ship, Just Read the Instructions, in the Atlantic Ocean.
The satellite deployed at 1 hour, 29 minutes after liftoff.
SpaceX recovered both halves of the rocket nose cone by fishing them out of the Atlantic, SpaceX engineer Siva Bharadvaj said.
The launch had been delayed for 15 minutes due to strong high-altitude winds that could have knocked the rocket off course.
The Space Force had delayed the launch from April due to health concerns for the launch crews amid the coronavirus pandemic.
"We have to get it right the first time, and protecting our people is just as important as cost, schedule and performance," Gen. John F. Thompson, commander of the Space Force's Space and Missiles Systems Center, said in a statement about the delay.
The military's GPS system also is used by civilians, guiding such everyday tools as Google Maps and Uber's ride-share locator service.
The satellite, GPS III SV03, is intended to augment and update the existing network, which has 31 spacecraft in a medium Earth orbit. The Space Force aims to keep the number of GPS satellites around 24 spacecraft, as older satellites are retired.
The Space Force has said the GPS system remains strong and fully operational despite the delay of the launch.
But military officials also said the GPS III system, when fully operational, will bring three times better accuracy and up to eight times improved anti-jamming capability than its predecessor.
The Space Force planned to launch more GPS III satellites in 2020, trying to ensure all members of the launch team remain well during the coronavirus pandemic.
Launch and assembly crews for the GPS missions are rehearsing and reducing the on-site crew size to provide adequate physical distancing, officials said.
Lockheed Martin builds and delivers the GPS satellites, which the Air Force has said are vital to U.S. and allied operations worldwide, with 4 billion users in financial, transportation, and agricultural applications.
The launch on Tuesday was the second National Security Space Launch mission using a SpaceX Falcon 9 rocket. It was the first such mission in which any launch provider has attempted to recover the first-stage booster, the Space Force said.