The sharks, who stayed for around a week, are the world's second largest fish.
They feed exclusively on plankton, which at this time of year, is not normally found in the North Sea.
National Trust Warden on the Farne Islands and marine specialist, Anthony Hurd commented: "These large plankton eaters can filter the equivalent of an Olympic sized swimming pool every hour and pose no danger to people or wildlife.
"It's only the seventeenth occasion that these large fish have been recorded in the North East, and the first time around the Farnes.
"It's fantastic to have them here."
Basking sharks have a distinctive profile when filtering plankton at the surface.
Their large triangular dorsal fin gives it the classic shark profile, however, when basking sharks appear, the fish's head and tail also shows clearly above the water, making it unmistakable.
These large animals are normally sighted off the south west coast of England and the north west coasts of England and Scotland during the summer months. In the winter they migrate to warmer waters.