DOVER — An announcement from Republican presidential nominee-to-be Donald Trump that Indiana Gov. Mike Pence will be his choice for vice president drew praise from Delaware Republican leaders Friday.

“Donald Trump’s selection of Gov. Pence to be his running mate is a strong strategic move,” state party Chairman Charlie Copeland said in a statement.

“The governor’s conservative credentials are unmatched. I don’t think there should be any question that Republicans

Charlie Copeland

have the winning ticket in 2016.”

Mr. Trump had also been considering New Jersey Gov. Chris Christie and former House Speaker Newt Gingrich, both of whom have some Delaware ties. Gov. Christie graduated from the University of Delaware, and Mr. Gingrich spent time campaigning in the state during his 2012 bid for the Republican presidential nomination.

Gov. Pence, who has a record of strong conservatism, endorsed Sen. Ted Cruz of Texas in April, although he also praised Mr. Trump at the time.

Rob Arlett, a Sussex County councilman who served as the Trump campaign’s Delaware chairman and will be at the Republican National Convention this upcoming week, called the choice a “fantastic decision,” saying Gov. Pence brings plenty of “executive experience” to the campaign.

“It exemplifies Mr. Trump’s desire to unify not only the Republican Party but the country,” Mr. Arlett said.

Mr. Trump had been set to announce his choice Friday but postponed a news conference after an attack in France killed more than 80 people. He tweeted out his choice of Gov. Pence after several media outlets reported the selection.

Republicans, including Delaware’s 16 delegates, will gather Monday in Cleveland, Ohio, for the four-day Republican National Convention where Mr. Trump will formally be selected as the party’s nominee for president.

Trump’s pick was aimed in part at easing some Republicans’ concerns about his temperament and lack of political experience. Pence spent six years in Congress before being elected governor and his demeanor is as calm as Trump’s is fiery. While some conservatives are skeptical of Trump’s political leanings, Pence has been a stalwart ally on social issues.

Rob Arlett

Yet Pence is largely unknown to many Americans. And his solidly conventional political background runs counter to Trump’s anti-establishment mantra.

The two men scheduled a news conference for today in New York to present themselves to America as the Republican team that will take on Hillary Clinton and her Democratic running mate in November. The duo will head to Cleveland next week for the Rpublican National Convention.

As Pence arrived for a private meeting with Trump Friday, he told reporters he “couldn’t be more happy for the opportunity to run with and serve with the next president of the United States.”

In choosing Pence, Trump appears to be looking past their numerous policy differences. The governor has been a longtime advocate of trade deals such as NAFTA and the Trans Pacific Partnership, both of which Trump aggressively opposes. Pence also has been critical of Trump’s proposed temporary ban on foreign Muslims entering the United States, calling the idea “offensive and unconstitutional.”

The reaction to the Pence choice from Republican officials was overwhelmingly positive.

“It was a pick that clearly shows he is pivoting to the general election,” said GOP chairman Reince Priebus, who was in the midst of an interview with The Associated Press when Trump announced his decision. “He is choosing a person who has the experience inside and outside Washington, Christian conservative, very different style that I think shows a lot of maturity.”

Pence, a staunchly conservative 57-year-old, served six terms in Congress before being elected governor and could help Trump navigate Capitol Hill. He is well-regarded by evangelical Christians, particularly after signing a law that critics said would allow businesses to deny service to gay people for religious reasons.

Clinton’s campaign moved quickly to paint him as the “most extreme pick in a generation.”

Clinton spent Friday holding meetings in Washington about her own vice presidential choice. Massachusetts Sen. Elizabeth Warren, a favorite of the far left and one of the Democrats’ most effective Trump critics, was seen in a car that left Clinton’s home.

Trump spent weeks weighing vice presidential contenders, including former House Speaker Newt Gingrich and New Jersey Gov. Chris Christie, and only zeroed in on Pence in recent days. In fact, the selection process appeared on the verge of sliding out of control in the final hours before the announcement, sparking speculation that Trump might be changing his mind.

Word that Pence would be joining the Republican ticket began trickling out in news reports Thursday before Trump had made a final decision or called Pence to offer him the job, according to a Republican familiar with the situation.

Trump was in California for fundraisers, separated from his closest aides, and was fuming about leaks that were viewed by the campaign as an attempt to pressure him into the decision.

Still, Trump called Pence Thursday afternoon to offer him the job and ask him to fly to New York for a Friday morning news conference. Pence accepted and boarded a private plane, along with his wife.

A few hours later, a huge truck barreled through a crowded holiday celebration in Nice, France, killing more than 80 people. With Pence sitting in a New York hotel, Trump decided to postpone the announcement.

The billionaire businessman then went on Fox News to say that he had not yet settled on his “final, final” choice. By Friday, plans were back on track. Trump sent out a Twitter message that he was pleased to announce Pence as his running mate. Moments later, one of Pence’s aides filed paperwork with the Indiana Secretary of State’s office withdrawing him from the governor’s race.

Pence was up for re-election, and state law prohibits candidates from being on ballots in two contests. Trump’s formal announcement came about an hour before Pence’s noon Friday deadline for withdrawing.

Since taking office in 2013, Pence has presided over Indiana’s improving economy and falling unemployment rate, which Republicans credit to the state’s low taxes, limited regulation and pro-business climate. Yet his popularity at home has tumbled and re-election was not guaranteed.

Gingrich, one of the finalists for the vice presidential spot, said he was “very comfortable” with Trump’s decision and praised Pence as someone who could help unite the party.

But as of Friday afternoon, Gingrich had yet to share his support with Trump himself. He told The Associated Press he had not received a call from Trump telling him he wasn’t getting the job.

The Associated Press contributed to this article.