The impact, in a volcanic plain called the Lake of Excellence, was photographed by observers on earth on Sunday.
Scientists hope the resulting cloud of dust and debris will provide clues to the geologic composition of the site.
Octavio Camino, the spacecraft operations chief, said at the European Space Agency’s mission control centre in Darmstadt, Germany: “That’s it, we are in the Lake of Excellence. We have landed.”
Minutes later, a video screen on the control room wall showed a picture of the bright flash from the impact relayed from an observatory in Hawaii.
Mission manager Gerhard Schwehm said: “It was a great mission and a great success and now it’s over.”
During its months in orbit around the moon, the spacecraft scanned the lunar surface from orbit and took high-resolution pictures.
But its primary mission was testing a new, efficient, ion propulsion system that officials hope to use on future interplanetary missions, including the BepiColombo mission to Mercury planned for 2013.
The engine, which uses electricity from the craft’s solar panels to produce a stream of charged particles called ions, generates only small amounts of thrust but only needs 80kg of xenon fuel.
The craft’s X-ray and infrared spectrometers have gathered information about the moon’s geology that scientists hope will advance their knowledge about how the moon’s surface evolved and test theories about how the moon came into being.
On Saturday, mission controllers had to raise the craft’s orbit by 600 metres to avoid hitting a crater rim on final approach.
Had the orbit not been raised the craft would have crashed one orbit too soon, making the impact difficult or impossible to observe.
The manoeuvre had to be carried out quickly in the early hours of Saturday and operations chief Camino admitted that “we were under some stress”.