An Israeli official said on condition of anonymity on Sunday that the deal had been reached but would be officially announced on Monday.
Israeli commandos attacked the Freedom Flotilla in international waters in the Mediterranean Sea on May 31, 2010, killing nine Turkish citizens and injuring about 50 other people. A tenth Turkish national later succumbed to the injuries sustained in the raid.
Ankara initially reacted with fury. It suspended its military ties with Israel and expelled the Israeli envoy from Ankara in September 2010 over Tel Aviv's refusal to apologize for the killings.
However, Turkey gradually engaged in not-so-public talks with the Israeli regime to mend ties. Since last December, the two sides have held several rounds of talks aimed at restoring the tense bilateral ties.
The United States was reportedly pushing the two sides to resolve the dispute. Israeli Prime Minister Benjamin Netanyahu traveled to the Italian capital, Rome, where negotiations are said to have been held, to meet US Secretary of State John Kerry on Sunday.
A Turkish official also said Turkey's Prime Minister Binali Yildirim is scheduled to talk about the deal at 1:00 pm (1000 GMT) in Ankara on Monday.
"The prime minister will talk about the contents of the Turkey-Israel agreement at tomorrow's press conference," the unnamed Turkish official said Sunday.
The deal is set to go before Israel's so-called security cabinet for approval on Wednesday.
The Israeli official said the agreement will lead to the restoration of ambassadors.
Among Turkey's key conditions for the reconciliation accord with Israel were an apology and compensations, which are said to have been largely met. However, the main hurdle to the agreement is reported to be the lifting of Israel's blockade on the Gaza Strip.
According to the Turkish daily Hurriyet, the two sides have reached a compromise on the issue, according to which Turkey will be allowed to send aid for Palestinians via Ashdod in the occupied territories rather than directly to Gaza.
According to Reuters, under the reported terms of the deal, Israel will allow the completion of a much-needed hospital in Gaza, as well as the construction of a new power station and a desalination plant for drinking water.
Earlier, reports circulating about an imminent deal between Turkey and Israel had angered the families of the victims of the 2010 raid.
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