The robotic vehicle rolled down a ramp lowered by the lander and on to the volcanic plain known as Sinus Iridum.
Earlier on Saturday, the landing module containing the rover fired its thrusters to perform the first soft landing on the Moon since 1976.
The touchdown in the Moon’s northern hemisphere marks the latest step in China’s ambitious space programme.
The lander will operate there for a year, while the rover is expected to work for some three months.
The Chang’e-3 mission landed some 12 days after being launched atop a Chinese-developed Long March 3B rocket from Xichang in the country’s south.
Xinhua news agency reported that the craft began its descent just after 21:00 Beijing time, touching down in Sinus Iridum (the Bay of Rainbows) 11 minutes later.
Chang’e-3 is the third unmanned rover mission to touch down on the lunar surface, and the first to go there in more than 40 years. The last was an 1,900lb Soviet vehicle known as Lunokhod-2, which was kept warm by polonium-210.
But the six-wheeled Chinese vehicle carries a more sophisticated payload, including ground-penetrating radar which will gather measurements of the lunar soil and crust.
The 260 lb Jade Rabbit rover can reportedly climb slopes of up to 30 degrees and travel at 660ft per hour.
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