The megalodon, which measured between 14 and 18 metres (46–59 feet) in length and weighed 100 tonnes, ruled the Earth's waters until it became extinct two million years ago.
"(The discovery of the fossils) is an event of great scientific significance," Spain's Oceanography Institute (IEO) said in a statement on Monday.
"They show that the biggest marine predator of all time lived, hunted and reproduced in these waters during that era."
The fossil deposits were found at the base of an undersea mountain some 2,000 metres deep during an ocean research campaign in Canary waters in October 2012.
But scientists had to wait till now to determine that the fossils didn't belong to other extinct shark, whale and sea cow species.
Based on the kind of teeth it possessed, IEO scientists believe the megalodon fed on large prey like whales, dolphins, turtles and seals.
It is thought to have been a great migrator found in all of the Earth's oceans.