The Herschel space telescope was switched off on Monday.
Controllers emptied the satellite's fuel tanks and commanded the observatory to sever all communications.
The BBC science correspondent said the craft is now in a slow drift around the Sun, about 2.14 million km from Earth.
Herschel was launched in 2009.
It was the most powerful observatory of its kind ever put in space. It gathered pictures and other data at far-infrared wavelengths that have transformed our understanding of star formation and galaxy evolution.
Astronomers will continue to scrutinise Herschel's pictures and make discoveries long into the future.
Many of its observations will also be followed up by other telescopes that are able to see some of the same wavelengths of lights.
The final command to turn off the communications transponder was sent from the European Space Operations Centre in Germany, at 12:25 GMT.
The BBC reports the radio message took six seconds to reach the observatory and a further six seconds for ground stations on Earth to confirm the loss of signal.
The European Space Agency's next space telescope will be Gaia, which is scheduled to launch in September. It will make the most precise map yet of the stars in the Milky Way Galaxy.