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The shuttle, with a crew of five Americans, a Canadian and a Russian, has brought 1.8 tonnes of equipment to the seven-storey space station, which was launched last year in a $60bn project and consists of only two rooms so far.
Shuttle commander Kent Rominger completed the docking smoothly and exclaimed: "We have capture."
Astronaut Daniel Barry added."The whole station looks beautiful, and we're happy to be visiting."
"The history of this moment shouldn't be lost on us," said Nasa's Frank Culbertson.
He pronounced the docking "a very significant event - one that we're going to repeat many, many times in the future".
Astronaut Chris Hadfield, watching from the Johnson Space Centre in Houston, Texas, told Discovery's crew: "You've made the first space station docking look effortless."
Supplies, including spare parts, computers, tools, water and clothes, will be used by future inhabitants who will stay on the space station for months at a time. The first are due to arrive next March.
Space shuttles have docked nine times with Russia's Mir station in recent years.
But this marked the first time since Skylab in the 1970s that Nasa has docked with its own space station.
Discovery is due to remain docked with the station until 3 June, before returning to Earth on 6 June.
This weekend, Barry and fellow astronaut Tamara Jernigan will perform a six-and-a-half hour space-walk to fix two cranes and other tools to the station's exterior.
And on Sunday they are due to enter the station for the first time, taking the supplies inside.