The 46-year-old billionaire's new rocket, the Falcon Heavy, is the most powerful since the shuttle system was first introduced, and its launch was widely considered to be a significant risk.
Speaking to reporters, he explained: "I had this image of just a giant explosion on the pad, a wheel bouncing down the road. But fortunately that's not what happened."
As a result of its successful launch, the Falcon Heavy is now recognised as the most capable launch vehicle available.
Musk explained that the performance of the new device is more than double that of the world's next most powerful rocket.
But, impressively, it is only one third of the cost.
Images of the launch - which also saw a space-suited mannequin strapped in the driver's seat, while a David Bowie soundtrack played on a loop - have already been beamed around the world.
And Musk has hailed the launch as a tremendous success.
He said: "That was epic. That's probably the most exciting thing I've ever seen, literally."
The lower segment of the rocket returned to Earth to attempt controlled landings, and they managed to land on the ground at almost the same time.
Meanwhile, the upper-stage of the rocket instead headed towards Mars' orbit.