That process began Sunday night as the rover and lander successfully took photos of each other and began transmitting them, Ma Xingrui, commander of the lunar program, said.
He said the mission is a "complete success," the official Xinhua News Agency reported.
On Saturday, the mission completed its lunar soft landing, the first such after the former Soviet Union carried out a similar landing in 1976. The only other country to achieve such success is the United States.
The craft used sensors to determine the best landing spot before descending the last 300 feet to the surface, Xinhua said. It touched down on a volcanic area known as Sinus Iridum, or the Bay of Rainbows, about 8:12 a.m. ET Saturday, 12 days after being launched Dec. 2 by a Long March-3B rocket.
The six-wheeled Yutu or Jade Rabbit moved to a spot about 30 feet from the lander before the photo session began, the Chinese news agency said.
The color images, transmitted via a deep space network designed by China, showed the Chinese national flag on Jade Rabbit, Xinhua said.
The rover is scheduled to survey the moon's geological structure and surface substances and look for natural resources for three months, while the lander will conduct exploration at the landing site for one year.
Xinhua said the rover separated from the lander and touched the lunar surface at 4:35 a.m. Sunday.
At the time of the launch, Chinese scientists said the Chang'e-3 mission was the most complicated and difficult one attempted by them. They said more than 80 percent of the technologies adopted in the mission were new.
The Chang'e-3 name was derives from an ancient Chinese myth about a woman named Chang'e, who after swallowing magic pills, took her pet white rabbit "Yutu" to fly toward the moon, where she became a goddess, and has been living there with the rabbit.
China sent its first astronaut into space in 2003, becoming the third country after Russia and the United States to achieve independent manned space travel.
China's top leaders and the Communist Party congratulated the success of the mission.