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It is the first time two SpaceX crew Dragons have been parked in space at the same time.
Shannon Walker, the space station's commander, said: 'We are so excited to have you aboard.
Although this was SpaceX's third crew flight for NASA, it was the first to use a vehicle which has flown before, an essential part of Musk's push to the moon and Mars.
The Dragon capsule was also used for SpaceX's first crew launch last May, while the Falcon rocket soaring Friday hoisted crew two in November.
ESA astronaut Thomas Pesquet of France, NASA astronauts Shane Kimbrough and Megan McArthur, and JAXA astronaut Akihiko Hoshide of Japan of Crew 2 (from left, in black shirts) assemble with Crew 1 for their welcome ceremony