Israel Prime Minister Binyamin Netanyahu has said he "expressed apology" to Turkey for any error that led to the death of nine Turkish nationals in 2010 in the Gaza flotilla incident.
Netanyahu also said on Friday that Israel has also agreed to compensate the families of the victims.
In a phone call between Netanyahu and Turkish Prime Minister Recep Tayyip Erdogan, the "two men agreed to restore normalisation between Israel and Turkey, including the dispatch of ambassadors and the cancellation of legal steps against IDF soldiers," the statement said.
"In light of Israel's investigation into the incident which pointed to a number of operational mistakes, the Prime Minister expressed Israel's apology to the Turkish people for any mistakes that might have led to the loss of life or injury and agreed to conclude an agreement on compensation/nonliability."
Netanyahu also told Erdogan that Israel had "substantially" lifted restrictions on the entry of civilian goods into the Palestinian territories, including Gaza.
During the phone call, Erdogan underlined the importance of strong cooperation and friendship between Turkey and Israel, his office said.
"Erdogan told [Israeli premier] Binyamin Netanyahu that he valued centuries-long strong friendship and cooperation between the Turkish and Jewish nations".
At a joint press conference with Jordan's King Abdullah II, President Barack Obama said his administration has worked for months to reach the deal.
Obama said that the "moment was right" for Israel and Turkey to resume diplomatic relations.
In a separate statement from the White House, Obama said the US "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".
Obama has reportedly arranged the call at Ben Gurion airport just before he left Israel for Jordan.
Al Jazeera's Nicole Johnston, reporting from Jerusalem, described Netayahu's apology as "an incredible development" adding that it would be seen as a "huge achievement" of the Obama administration.
Johnston also said that it is a "great win for Turkey," which has been demanding the apology.
Meanwhile, Al Jazeera's Elif Ural, reporting from Istanbul, said that Hamas has sent a message expressing disappointment that Turkey has accepted the apology.
On May 31, 2010, Israeli commandos boarded a flotilla of six humanitarian ships on their way to Gaza.
Nine Turkish activists were killed on the lead ship Mavi Marmara, sparking international condemnation and contentious diplomatic dispute between Israel and Turkey.
An inquiry into the incident said Israel broke international humanitarian and human rights law.
The inquiry, which was later endorsed by the United Nations Human Rights Council, found "clear evidence to support prosecutions" for crimes including "wilful killing; torture or inhuman treatment; wilfully causing great suffering or serious injury to body or health."
Al Jazeera's Anita McNaught, reporting from Cairo, said Turkey got "almost everything it wanted" from the apology, including acknowledgement of Israel's "operational errors" and offer of compensation.
"This is an extraordinary event and a completely unexpected one," our correspondent said. "This has been enormously damaging schism between these two countries [Israel and Turkey]".
Israel has imposed a blockade on the Gaza Strip since June 2007 after the Palestinian group Hamas took control of the territory.
Though the Israeli restrictions have been eased, Israel still enforces a naval blockade on the territory.
The lifting of the blockade, which Turkey has also demanded from Israel, is not covered in the apology, according to Al Jazeera's McNaught.