The car-size, one-tonne rover costing USD 2.5 billion touched down on Mars at 05:30 GMT (11:00 IST), NASA said.
The rover's descent-stage retrorockets fired, guiding it to the surface. Nylon cords lowered the rover to the ground in the "sky crane" manoeuvre.
When the spacecraft sensed touchdown, the connecting cords were severed, and the descent stage flew out of the way, according to NASA.
The landing was an unprecedented feat that involved penetrating the atmosphere at a speed of 21,240 kilometres per hour.
Minutes after touchdown, Curiosity beamed back the first pictures from the surface showing its wheel and its shadow, cast by the afternoon Sun.
Scientists have found signs of water on the red planet, though it is now a dry place with a thin atmosphere, extreme winters and dust storms.
Curiosity is not equipped to search for living or fossil microorganisms but it will look for basic ingredients essential for life, including carbon, nitrogen, phosphorous, sulphur and oxygen.
