Astronauts used the station's big robot arm to grab the capsule, as the craft flew 400 kilometres above Germany.
NASA's commercial shipper, Orbital ATK, named the spacecraft the SS John Glenn in honour of the first American to orbit Earth. It rocketed from Cape Canaveral, Florida, on Tuesday with nearly 7,700 pounds of food, experiments and other goods.
Glenn died in December at age 95 and was buried earlier this month at Arlington National Cemetery. His widow, Annie, granted permission for Orbital ATK to use his name for the Cygnus spacecraft. The company, in fact, sent up some memorabilia for the Glenn family.
Space station commander Peggy Whitson who on Monday will set a US record for most accumulated time in orbit notified Mission Control when the capsule was captured.
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"We're very proud to welcome on board the SS John Glenn," said French astronaut Thomas Pesquet, who took part in the operation. The contents "will be put to good use to continue our mission of research, exploration and discovery."
Whitson is making her third space station flight. Early Monday, she will surpass the 534-day, two-hour-and-change mark set by astronaut Jeffrey Williams last year. President Donald Trump will call her from the Oval Office to offer congratulations.
The SS John Glenn, meanwhile, will remain at the orbiting outpost until July, when it is let go to burn up in the atmosphere.