The naming of Sinwar to lead the Palestinian militant group came as Israel braced for potential Iranian retaliation over the killing of his predecessor Ismail Haniyeh last week in Tehran.
Speaking at a military base on Wednesday, Prime Minister Benjamin Netanyahu said Israel was "determined" to defend itself.
"We are prepared both defensively and offensively," he told new recruits.
Army chief Lieutenant General Herzi Halevi vowed to "find him (Sinwar), attack him" and force Hamas to find another leader.
Sinwar - Hamas's leader in Gaza since 2017 - has not been seen since the Oct 7 attack, which was the deadliest in Israel's history.lism.