The deal ends five years of enmity between two key Middle East nations after an Israeli raid on a Gaza-bound flotilla in 2010 that killed eight Turkish nationals and an American of Turkish origin.
There was no immediate comment from Turkish officials. Anadolu Agency, the semiofficial news source in Turkey, quoted diplomatic sources as saying talks were continuing.
As part of the framework agreement, Israel will set up a compensation fund for those who were killed or injured in the raid on the Turkish aid ship, the Mavi Marmara, while Turkey agrees to drop all legal claims against Israel, according to the Israeli officials.
Media reports in Israel placed the compensation fund at $20 million, but Israeli officials have not confirmed the amount.
In addition, the two countries will return their respective ambassadors to Ankara and Tel Aviv.
Turkey also agreed to prevent Hamas leader Saleh al-Arouri from operating within the country, according to the statement from Israeli officials. Arouri is a founding member of the al-Qassam Brigades, the military wing of Hamas.
Israel and Turkey will soon begin discussions about a natural gas pipeline between the countries as well as the sale of natural gas from Israel to Turkey, according to the officials.
"It all depends on the final signatures," said the statement from anonymous Israeli officials.
Israeli Prime Minister Benjamin Netanyahu in March 2013 apologized
for the raid during a phone call to his Turkish counterpart, Recep Tayyip Erdogan.
At the time of the call, Netanyahu was sitting with U.S. President Barack Obama in a trailer on a Tel Aviv airport tarmac. In the call, which Turkey's foreign minister said lasted nearly 30 minutes, Netanyahu acknowledged "operational mistakes" during the raid.
The apology signaled a thaw in relations but an agreement to fully normalize relations remained elusive.
Turkey and Israel have been two pro-Western political, economic and military linchpins in the Middle East, and their falling out has hurt initiatives to tackle problems in the region, such as the Syrian civil war and tensions relating to Iran's nuclear aspirations.
A Muslim member of NATO, Turkey long had been Israel's most significant Muslim friend, and the deterioration of relations between the two nations intensified the Jewish state's isolation in the region, more unstable in light of the Arab Spring and other troubles in the Middle East.
Erdogan's critical rhetoric toward Israeli policies in Gaza have been hailed by many in the Arab world.
Turkey withdrew its ambassador to Israel after the flotilla
incident and refused to resume normal diplomatic ties with the Jewish state without an apology and compensation for the victims' families.
An independent Israeli commission charged with investigating the raid concluded that the outcome was "regrettable" but legal under international law.
The raid triggered a wave of international condemnation of Israel and its policies toward Gaza.