Herschel observatory has run out of liquid helium to keep its instruments and detectors at their ultra-low functioning temperature. This equipment has now warmed, meaning the telescope cannot see the sky.
Herschel was launched in 2009 to study the birth of stars and the evolution of galaxies. It is sensitive to far-infrared and sub-millimetre light.
The BBC science correspondent said its 3.5m mirror and three state-of-the-art instruments made it the most powerful observatory of its kind ever put in space.
Controllers at the European Space Agency operations centre in Darmstadt, Germany, will run final tests on the spacecraft in the coming weeks before putting it in a slow drift around the Sun.
"We will switch off the transponder and the spacecraft will go silent," said Micha Schmidt, the Herschel spacecraft operations manager.
The BBC reports all the information gathered by the observatory is now being assembled into a public archive for future study.
''The telescope gathered images and information in such volume that astronomers have barely scratched the database,'' Professor Matt Griffin of Cardiff University told BBC News.
Engineers issued an alert early in March warning astronomers that observations were coming to an end.