Israel and Turkey agreed to restore full diplomatic ties after more than six years of animosity, clearing the way for renewed cooperation between the U.S. allies and an easing of Israel’s blockade of the Hamas-ruled Gaza Strip.

Officials from both countries said late Sunday that negotiators in Rome had reached a deal that will be made public in Jerusalem and Ankara on Monday. Israeli Prime Minister Benjamin Netanyahu was in Rome to meet with Secretary of State John Kerry and discuss the agreement.

At a briefing in Rome on Monday morning with Mr. Kerry, ​the Israeli leader called it an important step toward normalizing relations that would have​”immense implications” for Israel’s economy. He didn’t provide further details but was scheduled to speak at a news conference later in the day.

“It’s a positive step we wanted,” Mr. Kerry said. “We hope it’s the beginning of others.”

The push toward rapprochement came amid security threats to both nations—the Syrian conflict on their borders, the rise of the extremist group Islamic State and what many regional governments view as Iran’s assertive military and political posture.