The Crew Dragon capsule is an enhanced version of SpaceX's Dragon capsule, which has ferried cargo from Earth to the ISS on 16 previous occasions.
The Crew Dragon is expected to reach the space station Sunday morning, merely 27 hours after liftoff.
SpaceX's first crewed mission, which will fly NASA astronauts Doug Hurley and Bob Behnken, could happen by July, according to NASA's most recent schedule. Nevertheless, traditional business models are no longer sustainable and high-quality publications, like ours, are being forced to look for new ways to keep going.
SpaceX's live stream starts from 12am on March 1 and cycles through preparation stages and launch before the capsule goes into orbit. The more immediate goal is to avoid harming the space station and its three occupants: an American, Canadian and Russian.
In 2014, the U.S. space agency awarded contracts to SpaceX and Boeing for them to take over this task.
The Crew Dragon launched lifted off from Cape Canaveral at 7.49 am GMT, (2.49am EST).
For SpaceX, which Musk founded in 2002, sending an astronaut into orbit would be a culmination of years of hard work and high-risk investment.
From launch to splash landing, the mission is full of critical "firsts" for NASA's Commercial Crew program. Dragon 1 and attach it to the space station.
Both SpaceX's Crew Dragon and Boeing's Starliner were supposed to conduct their first test flights last August.
While NASA has continued to fly probes and robots into deep space, and has even landed on Mars, the inability to fly humans has remained an embarrassment for an agency that beat the Soviet Union in the Cold War space race to the moon. "Right now, the date is July and that's what we're planning for, but if we change that date we'll make sure people know when it's the right time".
While the Dragon spacecraft launched successfully Saturday, the mission still has several significant hurdles to clear. Musk said the redesigned capsule has "hardly a part in common" with its predecessor.
Despite SpaceX's success at recovering and reusing its rockets, NASA is insisting on brand new boosters from SpaceX for the crew capsule flights.
"People have gone to space station on Soyuz", he said this morning during a post-launch press conference here at NASA's Kennedy Space Center, referring to the handful of private citizens who have flown aboard Russia's Soyuz spacecraft (and reportedly plunked down between $20 million and $40 million apiece to do so). "And then re-entry", Musk said at a press conference, held in the Kennedy Space Center, when asked which stages of the Dragon 2 mission he anxious about most.