The deal, drafted at a secret meeting in Switzerland, calls for Israel to compensate victims of the raid, a return of envoys and the start of talks on gas exports to Turkey, the unnamed official said.
All Turkish lawsuits against Israel will be cancelled, and Turkey will prevent senior Hamas operative Salah Aruri from entering its territory and acting from there, the source added.
Israel has long accused Turkey of letting Aruri plan deadly attacks from its territory.
According to the official, incoming Mossad chief Yossi Cohen and Joseph Ciechanover, Prime Minister Benjamin Netanyahu's point-man for Turkish reconciliation, made up the Israeli team, with Turkish foreign ministry Undersecretary Feridun Sinirlioglu representing Ankara.
A separate official could not say when the pact might be signed, but Channel 10 television said it was expected "in coming days."
Turkish diplomatic sources, quoted by the state-run Anatolia news agency, said negotiations between Israel and Turkey on a normalisation of ties were in progress.
The talks were continuing with the aim of reaching a result for the normalisation of ties in the shortest possible time, the sources added.
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On Monday, Turkish President Recep Tayyip Erdogan, known for his angry outbursts at Israel, spoke in favour of normalising ties with Israel, which could benefit the Palestinians as well.
"We, Israel, the Palestinians and the region have a lot to win from a normalisation process," he said. "The interests of all the peoples of the region need to be considered."
In 2010, Israeli commandos stormed the Turkish-flagged Mavi Marmara, the largest ship in an aid flotilla for the besieged Gaza Strip.
Nine Turks died in the raid and one more, who was in a coma, died in 2014.
The assault sparked widespread condemnation and provoked a major diplomatic crisis between the two countries.
Ankara expelled the Israeli ambassador, demanded a formal apology and compensation, as well as an end to the blockade on the Gaza Strip, which is ruled by Hamas, a Palestinian militant group.
Talks on compensation began in 2013 after Israel extended a formal apology to Turkey in a breakthrough brokered by US President Barack Obama but had not been finalised.
Thursday's announcement comes just hours after Netanyahu signed a major natural gas deal aimed at tapping large deposits in the Mediterranean with a consortium that includes US firm Noble Energy.
Turkey is currently experiencing a major crisis in its ties with Russia, from which it buys more than half of its natural gas needs.