The two spacecraft are scheduled to be linked for a week, while the Discovery crew delivers food and supplies to the two men on the station.
The Discovery crew will also attempt to repair any damage caused when foam insulation fell from the fuel tanks during its launch.
NASA officials said at least one shard of protective foam “might have struck” a wing of Discovery when it was launched, but expressed confidence the craft would return safely to Earth.
Officials said the shuttle Atlantis can be launched to stage a rescue if needed, but that three more days are required to finish the damage assessments.
NASA administrator Michael Griffin told ABC television that all the indications were that Discovery “is in fact a clean bird”.
It may be the last visit for some time after NASA decided to ground its fleet in the wake of the latest set back.
Discovery’s astronauts have slowly inspected the shuttle’s wings and nose for possible damage, using a 30 metre movable arm with lasers and a camera mounted on its tip.
“Until we’re ready we won’t fly again,” said space shuttle program manager Bill Parsons.
It’s not known at this stage how that will affect the Discovery’s current mission.
NASA lead flight director Paul Hill said experts were still receiving and analysing the data from the inspection.
Discovery settled into orbit yesterday on the first shuttle flight since the Columbia disaster two and a half years ago.
Hours later, the space agency disclosed that an object believed to be a four centimetre piece of thermal tile appeared to have broken off from a vulnerable spot near the nose landing-gear doors on the underside of the shuttle.
The inspection was planned all along, before NASA discovered the chipped tile.
NASA stuck to its original work schedule and inspected only the nose and wings, examining the dozens of reinforced carbon panels that withstand the heat during re-entry into Earth’s atmosphere.
Mr Hill said the thermal tiles on the belly could be inspected Friday if engineers request a look.