Mount Sharp is a Mount-Rainier-size mountain at the centre of the vast Gale Crater and the rover mission's long-term prime destination.
"Curiosity now will begin a new chapter from an already outstanding introduction to the world," said Jim Green, director of NASA's Planetary Science Division at NASA Headquarters in Washington.
"After a historic and innovative landing along with its successful science discoveries, the scientific sequel is upon us," said Green.
Curiosity's trek up the mountain will begin with an examination of the mountain's lower slopes.
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"It has been a long but historic journey to this Martian mountain," said Curiosity Project Scientist John Grotzinger of the California Institute of Technology in Pasadena.
Curiosity currently is positioned at the base of the mountain along a pale, distinctive geological feature called the Murray formation.
Compared to neighbouring crater-floor terrain, the rock of the Murray formation is softer and does not preserve impact scars, as well. As viewed from orbit, it is not as well-layered as other units at the base of Mount Sharp.
In late 2013, the team realised a region of Martian terrain littered with sharp, embedded rocks was poking holes in four of the rover's six wheels.
This damage accelerated the rate of wear and tear beyond that for which the rover team had planned.
In response, the team altered the rover's route to a milder terrain, bringing the rover farther south, towards the base of Mount Sharp.
After landing inside Gale Crater in August 2012, Curiosity fulfilled in its first year of operations its major science goal of determining whether Mars ever offered environmental conditions favourable for microbial life.