The return of Mr. Brunson marked an end to a diplomatic standoff that jeopardized relations between the North Atlantic Treaty Organization allies—and was immediately embraced by Mr. Trump ahead of midterm elections that will determine whether his party retains control of Congress. Evangelical Christians, an important part of Mr. Trump’s base, closely followed Mr. Brunson’s plight.

Mr. Trump carried the release of Mr. Brunson with him to Kentucky hours after the meeting, celebrating it almost as soon as he took the stage.

“He is on American soil,” he told cheering supporters. “It wasn’t easy. That one wasn’t easy. And we don’t pay ransom.”

Conservative Christians backed Mr. Trump in huge numbers in the 2016 general election despite skepticism over his own record of conservatism. More than 80% of white evangelical and born-again Christians voted for Mr. Trump, according to national exit polling—a larger percentage than backed Mitt Romney, John McCain or George W. Bush, the GOP candidates in the previous three elections.

Both Mr. Trump and Vice President Mike Pence, an evangelical Christian himself, are now out on the campaign trail to ensure that the conservative Christian base turns out—not only to support Republicans in November midterm elections but also to lock in votes for re-election in 2020.

Mr. Brunson and his family met Saturday with Mr. Trump, Secretary of State Mike Pompeo and other White House officials and lawmakers who had helped engineer his release.

“From a Turkish prison to the White House in 24 hours. That’s not bad,” said Mr. Trump, with Mr. Brunson sitting next to him in the yellow chair normally reserved for visiting heads of state.

Over the summer, Mr. Brunson, a North Carolina-based teaching elder with the Evangelical Presbyterian Church, was moved from jail to house arrest.

The homecoming for Mr. Brunson unfolds in the shadow of the disappearance of Jamal Khashoggi, the Saudi journalist who hasn’t been seen since he entered a Saudi consulate in Istanbul on Oct. 2. Turkey has been looking for U.S. support in confronting Saudi Arabia over Mr. Khashoggi, who Turkish authorities allege was killed by Saudi operatives. Saudi Arabia has denied any involvement, and on Sunday it threatened to retaliate against any Trump administration punishment.

From Turkey’s perspective, freeing Mr. Brunson could also give the country more leverage with the U.S. over Saudi Arabia., U.S. officials said.

Sen. Lindsey Graham (R., S.C.), a member of the Senate Armed Services Committee, said in an interview: “This was a real barrier to having a normal relationship with Turkey. This allows us to move forward.”

Mr. Brunson was arrested in October 2016 and charged with supporting terrorist groups. He denied the accusations.

The Trump administration invested considerable strategic capital in freeing Mr. Brunson, using economic sanctions and stepped up public pressure when Turkey for months refused to release the pastor. Mr. Trump at a May White House meeting urged Turkish President Recep Tayyip Erdogan to release Mr. Brunson, and the president risked looking ineffectual had Turkey kept Mr. Brunson locked up.

In June, the U.S. imposed sanctions on Turkish ministers. While Mr. Erdogan denounced the measures, he also privately looked for ways to settle the dispute, Turkish officials said.

Mr. Trump denied that he had cut any deals to win Mr. Brunson’s release, though he made clear he anticipates that relations between the two countries will now improve.

“We’ve been negotiating long and hard,” Mr. Trump said. “We do not pay ransom in this country—at least any longer.” He didn’t elaborate.

At a hearing on Friday, a Turkish court found Mr. Brunson guilty of aiding terror groups but sentenced him to time served, setting in motion his trip home.

Write to Vivian Salama at vivian.salama@wsj.com and Peter Nicholas at peter.nicholas@wsj.com