The team of scientists spotted the great white (Carcharodon carcharias) in waters off Cabrera, an uninhabited island and nature reserve 11 miles south of Mallorca.
The shark measuring five metres (16.5ft) in length was filmed around 10am on Thursday morning by the team led by marine biologist Ricardo Sagarminaga van Buiten. The image was later uploaded onto the Facebook page of the Alnitak expedition 2018.
“In recent years there were possible unconfirmed sightings and various rumours, but this is the first scientific observation of the presence of the white shark in Spanish waters for at least 30 years."
Alnitak, a research and conservation project, said two 16-year-old students had been aboard and were among those who had witnessed the sighting.
Great whites are one of 46 species of shark reported in the Mediterranean, although sightings are incredibly rare.
.The more common Blue shark — tintorera in Spanish – have been blamed for closing beaches when their presence in detected close to the shore.