Spain's Civil Guard confirmed that the remains of a body were discovered on Sunday alongside a rucksack containing her identification.
The bones were found by a walker in a remote area of woodland off the path between Lluc and Pollenca in the north of the island.
Police believe she may have died after suffering a serious fall.
"Everything is pointing towards her suffering an accident while she was hiking, although this will need to be confirmed by the post-mortem," said a Guardia Civil statement.
Tennant failed to return to her hotel in Alcudia from a walk in the Tramuntana Mountains on October 9th 2007.
Her family made repeated appeals for information and travelled to the island several times to call for her disappearance to be properly investigated.
A spokesman for the British Embassy in Madrid said: "We are liaising with local authorities and providing consular assistance to the family of a British national who went missing in Majorca in October 2007."