The construction of the telescope, which also features a new generation of instrumental observation techniques, lasted for nine years, six years longer than planned.
Difficulties included hauling parts of the telescope weighing 400 tonnes to one of the world's best astrophysical observation sites at an altitude of 2,400 metres.
Roque de los Muchachos has clear nights and stable wind conditions, comparable to only a few other sites in Chile and Hawaii.
With its powerful mirror, the Grantecan may be able to see distant galaxies come into being, helping scientists to work on solving the riddle of the origins of the universe.
It could yield new information on the chemical components created by the Big Bang that gave birth to the universe 14 billion years ago, on black holes, and on dim planets that had gone undetected by less sophisticated equipment.
The Grantecan could even discover new planetary systems, and give clues to the question whether there is life on other planets.
The telescope, costing about 130 million euros ($180 million), was financed mostly by Spain, with partner universities in Mexico and United States covering around 10 percent of the cost.
Future telescopes are expected to have mirrors measuring up to about 40 metres in diameter, and Roque de los Muchachos is hoping to become home to one of them as well.