It will be the longest continuous stay anyone has had aboard the 250 mile-high orbiting platform.
The spacecraft docked successfully at 01:33 GMT on March 28, NASA annunced.
Scientists hope to get a keener idea of the effects on the human body of living in microgravity for extended periods.
The space agencies say the data will be invaluable as they plan towards eventually mounting a mission to Mars.
Scott Kelly and Mikhail Kornienko launched from Baikonur in Kazakhstan in a Soyuz vehicle at 01:42 local time on March 28.
They were joined on the flight up by cosmonaut Gennady Padalka, but his tour will only last the normal six months.
Although Scott Kelly and Mikhail Kornienko will set an endurance record for this space station, some of the stays aboard the old Russian Mir platform were much longer.
Four cosmonauts lived on Mir at various times for more than a year, with Valeri Polyakov spending a mammoth 437.7 days in orbit between 1994 and 1995.
“The last time we had such a long duration flight was almost 20 years and of course all… scientific techniques are more advanced than 20 years ago,” Mikhail Kornienko was quoted as saying by the AP wire service in the pre-launch press conference.
“And right now we need to test the capability of a human being to perform such long-duration flights. So this is the main objective of our flight – to test ourselves.”
Scott Kelly added: “One of the differences here is that we’re doing it as an international partnership, and if we’re going to go beyond low-Earth orbit again, perhaps to Mars, because of the cost and the complexity it will most likely be an international mission, so we see this as a stepping stone to that.”
Knowledge on how to mitigate some of the deleterious effects of living in zero-g has improved markedly since the Mir era, and the expectation is that Scott Kelly and Mikhail Kornienko will come back in a better shape than those early pioneers.
Programmed nutrition and exercise routines now prevent much of the bone density loss and muscle weakness that earlier astronauts used to experience.
However, there are other problems that doctors still need to study and understand. They have poor data on the effects on immune function, for example, and there is considerable concern about the damage spaceflight causes to the eyes. This is a newly recognized phenomenon, and appears to be related to the way fluid is redistributed in a weightless body.
Pressure is seen to build in the skull and on the optic nerve, and a large number of astronauts return to Earth complaining that their vision is not as good as when they went up.
By having Scott Kelly and Mikhail Kornienko onboard for a year, the agencies will be able to monitor how such complications progress beyond the normal six-month tour of duty.
Scott Kelly’s situation is made more interesting by the fact that he has an identical twin brother, Mark Kelly, who was himself an astronaut before retiring from NASA in 2011.
Scott and Mark Kelly will be used in a comparative study: one in space, one on the ground.
Relativity theories predict that Scott Kelly should age less quickly than his brother while speeding above the Earth – but only by a few milliseconds over the year.
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