Israeli President Isaac Herzog and his Turkish counterpart Tayyip Erdogan shake hands during a press conference in Ankara, in March. AFP
"It was decided to once again upgrade the level of the relations between the two countries to that of full diplomatic ties and to return ambassadors and consuls general from the two countries," said a statement from Lapid's office.
The Israeli prime minister hailed the diplomatic breakthrough as an "important asset for regional stability and very important economic news for the citizens of Israel".
The announcement follows months of bilateral efforts to mend ties which began to fray in 2008, following an Israeli military operation in Gaza.
Relations then froze after the deaths of 10 civilians following an Israeli raid on the Turkish Mavi Marmara ship, part of a flotilla trying to breach a blockade by carrying aid into Gaza in 2010.
A 2016 reconciliation agreement that saw the return of ambassadors all but collapsed in 2018-2019, when more than 200 Gazans were shot dead by Israeli forces during border protests.
During a landmark visit by Israeli President Isaac Herzog to Ankara in March, Turkish President Recep Tayyip Erdogan proclaimed the meeting marked "a turning point in our relations".
Israel did not immediately detail when its ambassador would be posted to Ankara.