Hayabusa means peregrine falcon in Japanese.
The probe will map the surface of the asteroid before touching down, deploying small explosives to blast a crater and then collect resulting debris.
Asteroids are believed to have formed at the dawn of the solar system and the probe's target is one called 1999 JU3, which scientists believe contains organic matter that may have contributed to life on Earth.
The probe is expected to arrive at the asteroid in mid-2018 and return with samples in 2020, the year that Tokyo hosts the Summer Olympic Games.
The mission should help Japan's space programme put a troubled past well behind it.
The first Hayabusa probe was unable to collect as much material as hoped but still made history by being the first vessel to bring back samples from an asteroid. Its seven-year mission ended in 2010 when it blazed a trail over Australian before slamming into the desert.
Both probes were developed by the Japan Aerospace Exploration Agency.
The first Hayabusa probe was launched on the domestically developed H-2A rocket, as was Hayabusa2. In 2003, an H-2A rocket carrying two spy satellites veered off course and had to be destroyed.
The Hayabusa2 launch was first scheduled for Nov. 30 but delayed twice by bad weather. The last chance for a successful launch before 2016 would have been December 7.
The European Space Agency's Philae probe finished a 57-hour mission on the surface of a comet on November 15, but lost battery power due to landing in a spot shielded from the sun it needed to charge the battery for an extended mission.
© Thomson Reuters 2014