The SpaceX cargo ship, called Dragon, eased up to the orbiting lab, and station astronauts reached out with a robot arm and snared it.
"Looks like we've tamed the Dragon," reported space station commander Sunita Williams. "We're happy she's on board with us."
Williams thanked SpaceX and NASA for the delivery, especially the chocolate-vanilla swirl ice cream stashed in a freezer.
The linkup occurred 250 miles above the Pacific, just west of Baja California, 2 1/2 days after the Dragon's launch from Cape Canaveral, Fla.
"Nice flying," radioed NASA's Mission Control.
It's the first delivery by the California-based SpaceX company under a $1.6 billion contract with NASA. The contract calls for 12 such shipments.
This newest Dragon holds 1,000 pounds of groceries, clothes, science experiments and other gear. It will remain at the space station for nearly three weeks before departing with almost twice that much cargo at the end of the month. Dragon is the only cargo ship capable of bringing back research and other items, filling a void left by NASA's retired shuttles.
SpaceX -- owned by PayPal's billionaire creator Elon Musk -- launched Dragon aboard a Falcon 9 rocket Sunday night. One of the nine first-stage engines failed a minute into the flight, but the other engines compensated and managed to put the capsule into the proper orbit. The mishap, however, left a secondary payload aboard the rocket -- an Orbcomm communication satellite -- in too low of an orbit.
This is the second Dragon to visit the space station. Last May, SpaceX conducted a test flight.
NASA is hiring out space station supply runs to American companies now that the shuttles are museum relics. The shuttle fleet was retired in 2011 after 30 years so the space agency could focus on human trips beyond low-Earth orbit; the destinations include asteroids and Mars.
Space station partners Russia, Japan and Europe also launch cargo ships, but those vessels are filled with trash and destroyed during descent. NASA scientists eagerly are awaiting nearly 500 samples of astronauts' blood and urine that have been stockpiled aboard the complex since Atlantis visited for the last time more than a year ago.
SpaceX is working to make its Dragon capsule safe enough to carry astronauts, possibly in three years. For now, NASA is paying the Russian Space Agency tens of millions of dollars to launch astronauts to the space station. Other U.S. companies also are vying for crew-carrying rights.
The space station currently houses three astronauts from America, Russia and Japan. Another American and two more Russians will arrive in two weeks.