Citing the Beijing Aerospace Control Center, Xinhua said the rover "has touched the lunar surface." The agency tweeted an image, apparently taken from the probe, showing the rover leaving tracks in the dust behind it as it rolled away.
Earlier, scientists burst into applause as a computer-generated image representing the Chang'e-3 probe was seen landing on the moon's surface via screens at a Beijing control centre, state broadcaster Chinese Central Television (CCTV) showed.
"Chang'e-3 has successfully carried out a soft landing on the moon. This makes China the world's third nation to achieve a lunar soft landing," the Chinese Academy of Sciences said in an online post on the mission's official page on Sina Weibo, a Chinese Twitter equivalent.
The landing came 12 days after blast-off and was the first of its kind since the former Soviet Union's mission nearly four decades ago.
Many Chinese took to the country's Internet message boards expressing joy at the news, which Xinhua described as a "historic breakthrough" in an emotional editorial.
"Space exploration is the cause of mankind, not just 'the patent' of a certain country," the commentary said.
"China will share the achievements of its lunar exploration with the whole world and use them to benefit humanity."
The editorial also cited President Xi Jinping's slogan for Chinese advancement, saying that the lunar bid "once again lights up the China Dream."
The landing marks the latest step in an ambitious space programme seen as a symbol of China's rising global stature and technological advancement, as well as the Communist Party's success in reversing the fortunes of the once-impoverished nation.
It comes a decade after the country first sent an astronaut into space, and ahead of plans to establish a permanent space station by 2020 and eventually send a human to the moon.
News of the landing quickly made an impact on China's hugely popular Internet message boards, with the words "Chang'e-3 lunar landing" racing to the top of the list of searched items on Weibo just minutes after touchdown.
"Congratulations on Chang'e-3's successful lunar landing. Long live China!" said one netizen.
Another said: "Felt so excited when it landed!"
The probe touched down on an ancient 400-kilometre (250-mile) wide plain known in Latin as Sinus Iridum, or The Bay of Rainbows.
The landing was previously described as the "most difficult" part of the mission by CAS on Chang'e-3's Weibo site.
The probe used sensors and 3D imaging to identify a flat surface. Thrusters were then deployed 100 metres (330 feet) from the lunar surface to gently guide the craft into position.
The landing process started at 9:00 pm (1300 GMT) and lasted for about 12 minutes.
Karl Bergquist, the international relations administrator at the European Space Agency who has worked with Chinese space officials on the mission, told AFP the key challenge was to identify a flat location for the landing.
The rover will spend about three months exploring the moon's surface and looking for natural resources.
It can climb slopes of up to 30 degrees and travel at 200 metres per hour, according to the Shanghai Aerospace Systems Engineering Research Institute.
The Chang'e-3 mission is named after the goddess of the moon in Chinese mythology, and the rover vehicle is called Yutu after her pet.
Yutu's name was chosen in an online poll of 3.4 million voters.
"China wants to go to the moon for geostrategic reasons and domestic legitimacy," said China space expert Joan Johnson-Freese, a professor of national security affairs at the US Naval War College in Newport, Rhode Island.
"With the US exploration moribund at best, that opens a window for China to be perceived as the global technology leader -- though the US still has more, and more advanced, assets in space."