For President-elect Donald J. Trump, the cease-fire agreement between Israel and Gaza was crucial for two reasons.

It removed one of the most vexing international conflicts that had been hovering at the start of his second term and gave Mr. Trump, known during his days in New York as a “real estate guy,” something to claim early victory — even if it happened before he took office.

In a post on social media on Wednesday, Mr. Trump said the deal “happened only as a result of our historic victory in November.”

The outlines of the deal were not particularly different from what President Biden sought in May. But multiple people with insight into the process said Mr. Trump’s victory in November, along with the involvement of members of his new administration, was key to moving things forward.

After the deadly Oct. 7, 2023, attacks by Hamas have been the backdrop for the 2024 US presidential race. As Mr. Trump has emerged not only as the Republican nominee but also as a survivor of the July assassination attempt, his relationship with Israeli Prime Minister Benjamin Netanyahu has improved. . (Ties broke after Mr Netanyahu congratulated Mr Biden on winning the 2020 election.)

Fear of what the often unpredictable Mr. Trump — who said months ago that the world knows he is “crazy,” using an expletive for emphasis — might do on the world stage has become a key theme in private conversations among foreign leaders.

So the deal — struck with significant input from Mr. Trump’s Middle East envoy, Steve Witkoff — allowed Mr. Trump to begin his term with one less problem.