The duo entered the ISS at 1:02 pm Eastern Time (1702 GMT) Wearing black polo shirts and khaki pants.
A day after a SpaceX rocket carrying two NASA astronauts lifted off from the Kennedy Space Centre in Florida, the Indian Space Research Organisation on Monday congratulated the two organisations and termed the manned space mission as "historic."
"Congratulations to #NASA and #SpaceX for historic first launch of manned mission after 2011. Great job !" ISRO tweeted.
On Sunday, SpaceX's Dragon spacecraft with NASA astronauts Bob Behnken and Doug Hurley successfully docked with the International Space Station.
The duo entered the ISS at 1:02 pm Eastern Time (1702 GMT) Wearing black polo shirts and khaki pants. They were greeted by fellow US astronaut Chris Cassidy, as well as cosmonauts Anatoli Ivanishin and Ivan Vagner.
The mission was the first between a private and a government-funded organisation, heralding the dawn of commercial space travel. The launch on Saturday also assumes significance as it was the first manned flight from US soil in nearly a decade.
India has also been preparing the ground for its first manned space mission, "Gaganyaan". The Rs 10,000-crore ambitious project is expected to be launched in 2022, the year of the 75th anniversary of India's Independence. Four Indian Air Force fighter pilots selected as potential candidates for the mission are currently undergoing training in Moscow.