The docking began at 1051 GMT, more than 248 miles (400 kilometers) above the Earth's surface, north of New Zealand - and 27 hours after the capsule's launch on a SpaceX Falcon 9 rocket from the Kennedy Space Center at Cape Canaveral in Florida.
SpaceX's Crew Dragon is the first commercially built and operated American spacecraft designed for human passengers to dock at the space station.
This photo provided by SpaceX shows a life-size test dummy along with a toy that is floating in the Dragon capsule as the capsule made orbit. TV cameras on Dragon as well as the station provided stunning views of one another throughout the rendezvous.
As the capsule closed in on the space station, its nose cap was wide open like a dragon's mouth to expose the docking mechanism. SpaceX's new crew capsule arrived at the International Space Station, acing its second milestone in just over a day.
The white, bullet-shaped Dragon capsule, developed by Elon Musk's SpaceX company under contract to NASA, closed in on the orbiting station almost 260 miles above the Pacific Ocean and, flying autonomously, linked up on its own, without the help of the robotic arm normally used to guide spacecraft into position.
They burst into applause again, several minutes later, when the Dragon's latches were tightly secured. The test dummy was nicknamed Ripley after the main character in the "Alien" movies.
Like Ripley, the capsule is rigged with sensors to measure noise, vibration and stresses, and to monitor the life-support, propulsion and other critical systems throughout the flight.
The Dragon capsule will remain on the ISS until Friday before detaching to splash down in the Atlantic.
The Saturday morning launch went off without a hitch, much to SpaceX CEO Elon Musk's relief.
NASA says that Boeing's CST-100 Starliner continues to undergo testing in preparation for its Orbital Flight Test, slated for no earlier than April. Astronauts have been stuck riding Russian rockets ever since NASA's space shuttle program ended in 2011.
It pays Russian Federation to get its people up to the ISS orbiting research facility at a cost of $82 million per head for a round trip.