With flight commander Steve Lindsey at the helm, the US space shuttle linked up with the station at 28,000kph, 357km above the Pacific.
Two hours later, hatches between Discovery and the station were opened and the shuttle crew went through tunnels to be greeted by the station commander, Pavel Vinogradov, and Jeffrey William, a flight engineer.
The shuttle crew will deliver more than 2,272kg of equipment and supplies to the station before departing on July 14. It will leave behind Thomas Reiter, a German astronaut, for a six-month stay.
Piers Sellers and Michael Fossum, shuttle crew members, will perform spacewalks to repair a station transport system needed to complete construction of the half-finished $100 billion outpost.
Before docking, Lindsey manoeuvred the shuttle through a slow back-flip while Williams and Vinogradov photographed heat-resistant tiles on Discovery's underside that protect it during re-entry.
The photographs are part of the continuing inspection process that began at Discovery's launch from Florida on Tuesday. No significant damage has been found.
Nasa officials hope that this indicates that they have solved the problem of falling foam from shuttle fuel tanks that caused the loss of Columbia in 2003 and appeared again in the first post-Columbia shuttle flight last summer.
Another accident or serious problem could ground the shuttle fleet permanently before its planned retirement in 2010.
That, in turn, would mean that space station construction, which depends on the shuttle transport capabilities and has been on hold since Columbia, could not be finished.
Nasa hopes to fly 16 shuttle missions to complete the station before the spacecraft it has flown since 1981 is phased out.
Nasa coverage of shuttle mission: http://www.nasa.gov/mission_pages/shuttle/main/index.html