Planning for the telescope began in 1987 and has involved more than 1,000 people from 100 companies. It was inaugurated Friday by King Juan Carlos.
The observatory is located at 2,400 meters (7,870 feet) above sea-level where prevailing winds keep the atmosphere stable and transparent, the Canary Islands Astrophysics Institute said.
The institute, which runs the telescope, said it will capture the birth of stars, study characteristics of black holes and decipher some of the chemical components of the Big Bang.
The telescope is composed of 36 separate mirrors that began slowly focusing in July 2007 to eventually act as a single large reflecting surface that directs light onto a central camera point.
Among those who have done research at La Palma is Brian May, lead guitarist of rock group Queen, who studied there for part of his doctorate in astrophysics at the institute.
May, who published "BANG! The Complete History of the Universe" with astronomers Patrick Moore and Chris Lintott, composed a musical score for the telescope's inauguration.
Large reflecting telescopes began making major contributions to astronomical research when Edwin Hubble perfected the technique of capturing photographic exposures of space with the then-massive 200-inch mirror at Mount Palomar Observatory, in north San Diego County, California in Jan. 1949.
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Associated Press Writer Harold Heckle in Madrid contributed to this report.