The shuttle performed a backflip before docking so the ISS two-person crew could inspect ceramic tiles on its underbelly for damage, after concerns over foam pieces that came loose during lift-off.
The protective tiles form part of Discovery's heat shield, which is vital in protecting it during its descent to Earth.
The International Space Station's two residents warmly greeted the Discovery shuttles seven astronauts as they floated inside the ISS, on day three of a pivotal mission for the future of the station and US space ambitions.
"Great job on the rendezvous and good luck with your work on the ISS," a mission control official at the Johnson Space Centre in Houston, Texas, told the astronauts as the hatch was opened.
The astronauts went right to work after entering the ISS, preparing the shuttle's robotic arm to transfer a container filled with much-needed supplies and equipment for the space station.
Backflip
Before docking, Commander Steven Lindsey carefully flipped the shuttle to show Discovery's underbelly to the ISS crew, about 180 metres below the space station and hundreds of kilometres above Spain.
ISS crew members Pavel Vinogradov of Russia and Jeffrey Williams of the United States used digital cameras to photograph the heat shield that protects the shuttle during its re-entry into Earth's atmosphere.
The images will be analysed by NASA to find any cracks in the shuttle's heat shield in just the second flight since the 2003 Columbia accident, which was caused by damage to the shuttle's defences.
Live pictures of the docking were broadcast around the world as it began, with each craft travelling at about 28,000 kilometres per hour.
Vinogradov and Williams were seen shaking hands and smiling right after Discovery docked to their space home.
Apart from bringing critical supplies and equipment to the space station, the Discovery crew also will drop off their seventh passenger, European Space Agency astronaut Thomas Reiter of Germany, who will remain in the ISS for a six-month stay.
The nine-minute, 360-degree shuttle manoeuvre is among several measures NASA has taken to increase safety for its astronauts since seven of them died in the Columbia disaster.
The shuttle disintegrated on its return to Earth after its heat shield was pierced by debris during lift-off.
The back flip was first performed by Commander Eileen Collins last year in the first post-Columbia flight.
If Discovery is found to have sustained damage, NASA Administrator Michael Griffin has said the crew would abandon ship and take refuge inside the ISS while awaiting a rescue.
Pictures taken by the Discovery crew on Wednesday gave the US space agency early indications that the shuttle's nose and wing leading edge have not been damaged.
NASA officials have described the vessel as "clean", however said a final report on the images will be presented on Thursday.
Crucial mission
The current mission, aimed at showing whether safety improvements have succeeded, is key for the future of the shuttle program.
Any major incident would probably lead to an early end to the 25-year-old fleet, Mr Griffin has said.
NASA's chief wants to make space flight safer in order to resume regular shuttle missions - about four a year - to complete the ISS before Discovery, Atlantis and Endeavour are retired in 2010.
The space station is an essential part of US ambitions to send humans to Mars, as it would serve as a stepping stone for space exploration, Mr Griffin said.
It would also help scientists better understand the effects of long-term trips in space, he said.
Discovery is delivering critical cargo to the ISS, including a new oxygen generator for the space station that would accommodate crews of six people - double the current number - on the station starting in 2009.
British-born astronaut Piers Sellers, a naturalised US citizen, and fellow mission specialist Mike Fossum will perform two spacewalks and possibly a third if the 12-day mission is extended by a day.