"And that is confirmed capture," said a NASA commentator as space station's robotic arm grabbed the spaceship at 6:52 am.
The spaceship blasted off Monday from Cape Canaveral, Florida, carrying food, science experiments and other gear for the astronauts living in orbit.
It is the 12th mission for SpaceX under a $1.6 billion contract with NASA.
A key part of the cargo is a sophisticated supercomputer made by Hewlett Packard Enterprise (HPE), called The Spaceborne Computer.