The SpaceX cargo ship, called Dragon, eased up to the orbiting lab, and station astronauts reached out with a robot arm, snared it and firmly latched it down.
"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 ice cream.
The linkup occurred 250 miles above the Pacific, just west of Baja California, two and one-half days after Dragon's launch from Cape Canaveral, Fla.
The company's $1.6 billion contract with NASA calls for 11 more shipments.
This newest Dragon holds 1,000 pounds of groceries, clothes, science experiments and other gear. Williams and her crew won't get access to all that until today, when the hatch is opened.
The vessel 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 Pay-Pal'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.