Sakir Ozkan Torunlar, a veteran diplomat who had served as Turkey's consul general in Jerusalem between 2010 and 2014, was named to the post in a presidential decree late on Friday, Turkish media reported.
Israel's foreign ministry announced in September that Irit Lillian, who had been in charge of the Israeli embassy in Ankara for the past two years, would be the country's ambassador to Turkey.
Turkish Foreign Minister Mevlut Cavusoglu visited Israel in May this year and outgoing Israeli Prime Minister Yair Lapid travelled to Turkey the following month.
Ties between the two countries soured following a 2010 Israeli raid on an aid ship to Gaza that killed 10 Turkish citizens.
Diplomatic relations were restored in 2016, but two years later Turkey recalled its diplomats from Israel and expelled Israeli envoys when Israeli forces killed several Palestinians who took part in protests in Gaza.
Turkish President Recep Tayyip Erdogan criticised Israel's policy towards Palestinians under former prime minister Benjamin Netanyahu, who is set to return to office.
But Mr Erdogan sent a congratulatory letter to Mr Netanyahu after his victory in the Israeli general election held earlier this month.
Speaking a day after the November 2 election, the Mr Erdogan told Turkish broadcaster ATV: “Whatever the election result, we want to maintain relations with Israel on a sustainable basis, based on mutual respect for sensitivities and common interests.”