It will be attached to the ISS next weekend and will be there for two years so astronauts can see how it copes with space debris and solar radiation.
The Dragon was orbiting at a distance of 250 miles above the Earth and was captured by the ISS astronauts using a robotic arm. Nasa envisions inflatable habitats on Mars in a couple of decades while Bigelow Aerospace aims to launch a pair of inflatable space stations for commercial lease in four years.
It holds 3,175kg of freight, including the inflatable pod built by Bigelow Aerospace.
SpaceX's unmanned Dragon cargo ship, carrying lettuce seeds, laboratory mice, and an inflatable pop-up room, arrived on Sunday at a crowded International Space Station where six spacecraft are now docked.
The technology could lead to more efficient spacecraft designs, provide more room on long-duration missions, and possibly help Earthlings establish the first settlements on Mars.
Mr. Musk, the founder and chief executive officer of SpaceX, said: "The rocket landed instead of putting a hole in the ship - or tipping over - so we're really excited about that".
For now, the Bigelow expandable activity module will remain mostly off-limits to the station crew. In pursuit of that objective, the space agency has hired United States companies such as SpaceX to deliver cargo and, as early as next year, astronauts to the space station. As a result, "Dragon's arrival marks the first time two commercial cargo vehicles have been docked simultaneously at the space station", NASA said. Following stage separation in Friday's mission, the first stage of the Falcon 9 attempted again an experimental landing on the "Of Course I Still Love You" droneship in the Atlantic Ocean. SpaceX was returned to flight status after the disaster and its latest resupply mission to the ISS has been completed without any issues.
During the March 22 launch from Cape Canaveral of an Orbital ATK Cygnus cargo craft to the International Space Station, the rocket's Aerojet Rocketdyne upper stage engine fired for an extra minute to salvage a successful launch. It is expected to fly home next month with biological samples collected during former NASA astronaut Scott Kelly's recent yearlong mission and with bulky spacesuit components that engineers want to analyze on the ground.