Benjamin Netanyahu also agreed with Turkey’s PM Recep Tayyip Erdogan to compensate the families of the nine activists who were killed.
Israel’s prime minister had previously only expressed regret for the deaths.
The deal was brokered by US President Barack Obama during his visit to Israel.
Recep Tayyip Erdogan’s office said he had accepted the apology, “in the name of the Turkish people”.
In the past, Recep Tayyip Erdogan has always given two conditions for restoring bilateral relations with Israel – an apology and compensation for victims’ families.
Nine people were killed on board the Turkish aid ship, Mavi Marmara, when it was boarded by Israeli commandos while trying to transport aid supplies to Gaza in May 2010 in spite of an Israeli naval blockade.
The Israeli government admitted mistakes were made in intelligence-gathering and planning, but insisted its commandos used lethal force because activists had attacked them.
The activists said the troops had opened fire as soon as they boarded the vessel, which was in international waters at the time.
The incident provoked an international outcry and led to a major deterioration in relations between Turkey and Israel.
Before departing for Jordan on Friday afternoon, Barack Obama revealed that Benjamin Netanyahu and Recep Tayyip Erdogan had just spoken by telephone.
“The United States deeply values our close partnerships with both Turkey and Israel, and we attach great importance to the restoration of positive relations between them in order to advance regional peace and security,” President Barack Obama said in a statement released by the White House.
A statement issued by Benjamin Netanyahu’s office said that in the telephone conversation with Recep Tayyip Erdogan he had expressed regret over the deterioration in bilateral ties and noted his “commitment to working out the disagreements in order to advance peace and regional stability”.
“The prime minister made it clear that the tragic results regarding the Mavi Marmara were unintentional and that Israel expresses regret over injuries and loss of life,” it added.
“In light of the Israeli investigation into the incident, which pointed out several operational errors, Prime Minister Netanyahu apologized to the Turkish people for any errors that could have led to loss of life and agreed to complete the agreement on compensation.”
The two leaders had also agreed to continue to work on improving the humanitarian situation in the Palestinian Territories, the statement said.
A statement from Recep Tayyip Erdogan’s office said the two prime ministers had agreed on making arrangements for compensation for families of the dead activists.
“Erdogan told Benjamin Netanyahu that he valued centuries-long strong friendship and co-operation between the Turkish and Jewish nations,” it added.
Benjamin Netanyahu’s change of heart is a clear indication of the diplomatic clout that the US still wields with its two key allies in a turbulent region.
The prime minister’s call to his Turkish counterpart was apparently made from a trailer at Tel Aviv airport while Air Force One sat on the ground waiting to depart.
The unglamorous setting and the last-minute nature of the call suggests the deal may not have been easy to broker.
Israeli officials said the apology had become possible after Recep Tayyip Erdogan qualified earlier comments about Zionism in an interview with a Danish newspaper.
Benjamin Netanyahu expressed “appreciation” for the comments, his office said.
Former Israeli Foreign Minister Avigdor Lieberman called the decision to apologize a “serious error”, Israeli news site Walla reported.
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