The launch is broadcast on the company's website.
The launch took place as part of the Inspiration4 program, which was the first fully commercial astronaut mission in orbit.
The Falcon 9 launch vehicle was launched at 20:02 US East Coast time (03:02 Moscow time) from the spaceport at Cape Canaveral (Florida).
Earlier it was reported that SpaceX's American Dragon spacecraft successfully docked to the International Space Station (ISS).