The Dragon capsule, which was propelled into space by a Falcon 9 rocket, contained 2,500 kilograms of cargo, including 1.2 million tomato seeds.
And although an external cable that normally detaches during launch dangled from the capsule, it did not interfere with the docking.
A flight controller radioed from Houston's Johnson Space Centre: "Well done, well captured".
"That looked really, really cool in the night sky", said Hans Koenigsmann, a SpaceX vice president who left his launch control seat to run outside and watch.
That's when Canadian astronaut David Saint-Jacques will be pressed into duty, manning the Canadarm 2 to perform his first-ever "cosmic catch" manoeuvre, backed up by NASA astronaut Nick Hague.
Mr Saint-Jacques replied: "To all the teams around the world, we welcome to the ISS the Dragon spacecraft".
SpaceX launched the capsule Saturday from Cape Canaveral, Florida.
Making its second visit to the space station, the reusable Dragon capsule's pressurised cabin was packed with food, clothing and personal items for the crew, spare parts, computer gear and 725kg of science equipment and research material.
This is SpaceX's 17th delivery to the space station; the first was in 2012.
The science experiments included on this mission will enable space travelers to gauge Earth's Carbon dioxide from space, explore how microalgae may improve reusing on board the space station, accelerate "organ on chip" experiments and study regolith - the dusty, fragmented debris covering asteroids and moons.
The Dragon is the third cargo ship launched to the space station so far this year following a Russian Progress that reached the lab April 4 and a Northrop Grumman Cygnus that was attached to the central Unity module on April 19. The Dragon is the only cargo ship able to return to Earth in one piece.