Sunday's successful launch was preceded by the cancellation of four previous scheduled launches that were scheduled last week, including the one on Saturday.
It would have marked SpaceX's first so-called National Security Space mission, as defined by the USA military, SpaceX said.
The launch is a landmark for SpaceX to make a presence in the lucrative military space launch market.
Elon Musk's SpaceX capped a record-setting year on Sunday when it launched a rocket carrying a new GPS III satellite for the US Air Force, after delaying the mission several times because of a technical issue involving its rocket sensors and bad weather.
The GPS III satellite is a next-generation version satellite that will significantly aid the US Air Force in more precise geolocation services.
Space X rocket carrying USA military took off from Cape Canaveral from Florida on Sunday making the first-ever transportation of the security space transportation of the United States successful.
SpaceX has launched payloads for the U.S. military before, but Vespucci is the company's first official "National Security Space" mission - a designation reserved for liftoffs deemed critical to national defense.
The Air Force said that the launch was originally scheduled for 2014 but has been hobbled by production delays.
The rocket, which was carrying a satellite worth roughly $500m (£393.7m) built by Lockheed Martin, blasted off from Florida just before 2pm GMT. The rocket is carrying the U.S. Air Force´s most powerful Global Positioning System satellite ever built. It dropped the lawsuit in 2015 after the Air Force agreed to open up competition.
The successful GPS III SV01 mission marked SpaceX's 21st and final launch of 2018, beating the company's 2017 flight rate of 18 launches.
The next GPS III satellite is due to launch in mid-2019 and the subsequent satellites will undergo testing in the company's Colorado processing facility.
He has been a technology writer since more than five years.