WASHINGTON — Pete Buttigieg was a teenager, not yet openly gay, and had dreams of being an airline pilot when he watched Republicans in the late 1990s deny a confirmation vote to President Bill Clinton’s choice for ambassador to Luxembourg because of his sexual orientation.

Senator Trent Lott, Republican of Mississippi, the majority leader at the time, called homosexuality a sin and compared it with personal problems like alcoholism, kleptomania and sex addiction. Blocked by his adversaries, Mr. Clinton used a recess appointment to send James Hormel, a San Francisco philanthropist and heir to a meatpacking fortune, overseas.

Now, two decades later, Mr. Buttigieg, the former mayor of South Bend, Ind., and earlier this year a primary race opponent of Joseph R. Biden Jr.’s, is poised to become the first openly gay cabinet secretary after Mr. Biden, now the president-elect, picked him to run the Transportation Department. Mr. Buttigieg recalled the teenage memory during brief remarks on Wednesday.

“I watched that story, and I learned something about some of the limits that exist in this country when it comes to who is allowed to belong,” he said. “But just as important, I saw how those limits could be challenged.”

With Mr. Biden seated nearby during his remarks, Mr. Buttigieg recalled proposing to his husband, Chasten Buttigieg, in an airport terminal — “Don’t let anybody tell you that O’Hare isn’t romantic,” he joked — and thanked the president-elect for not wavering from the history-making nomination.

“I can’t help but think of a 17-year-old somewhere who might be watching us right now, somebody who wonders whether and where they belong in the world, or even in their own family, and I’m thinking about the message that today’s announcement is sending to them,” Mr. Buttigieg said.

History was clearly on Mr. Biden’s mind, as well. Even as he has been buffeted by the demands of Democratic interest groups over the past several weeks, the president-elect said he remained determined to assemble a cabinet that was not only qualified but also mirrored the diversity of the United States’ population.

Mr. Biden, who seemed annoyed by public and private criticism of his choices so far, said that when he was finished, he would have “a cabinet of barrier-breakers, a cabinet of firsts” unlike any of his predecessors’.

“We’ll have more people of color than any cabinet, ever. We’ll have more women than any cabinet, ever,” he said, noting that he has picked the first Black defense secretary, the first Latino head of homeland security, the first woman of South Asian descent to lead the budget office and the first woman to be Treasury secretary, among others. “Our cabinet doesn’t just have one first or just two of these firsts, but eight precedent-busting appointments.”

“And today,” he added, “a ninth.”

There has never been an openly gay cabinet secretary. Under President Trump, Richard Grenell, who is openly gay, served as acting director of national intelligence, a cabinet-level post that is not part of the 15 cabinet posts defined by federal law. He also did not face Senate confirmation because Mr. Trump chose to make him an acting director.

At 38, Mr. Buttigieg would also be one of the youngest cabinet secretaries in history. Julián Castro was 39 when President Barack Obama appointed him housing secretary in 2014. And Alexander Hamilton was in his mid-30s when he became the nation’s first Treasury secretary.

Like both of those men, Mr. Buttigieg has higher ambitions. His bid for the presidency this year vaulted him from obscurity into the top tiers of the Democratic Party. Now, he will have a national platform from which to continue building a political identity.

But that may put him in direct competition with Vice President-elect Kamala Harris, 56, who also challenged Mr. Biden for the Democratic presidential nomination and is all but certain to run for president again, perhaps as soon as 2024, when it is expected that Mr. Biden will not seek another term.

The pair expressed nothing but warmth toward each other on Wednesday, at an event in Wilmington, Del. Ms. Harris, who joined the event via video because of a winter storm on the East Coast, called Mr. Buttigieg a “trailblazing leader from the industrial Midwest who understands we need to create opportunity for people of all backgrounds.” Mr. Buttigieg thanked the vice president-elect for “your trailblazing leadership, your encouragement and your friendship.”

The good feelings might evaporate quickly if Mr. Buttigieg and Ms. Harris end up facing off against each other in a primary campaign that could begin in just over two years. Or Mr. Buttigieg could defer to Ms. Harris, waiting until he has a clearer path to the White House.

Mr. Biden called Mr. Buttigieg “a policy wonk with a big heart” and said he “selected Pete for transportation because the department is at the intersection of some of our most ambitious plans to build back better.”

If Mr. Buttigieg wins confirmation as transportation secretary, Mr. Biden said he would play a key role in advancing his ambitious agenda to rebuild the nation’s infrastructure and would be a central official in the administration’s efforts to combat climate change.

Mr. Buttigieg supports restoring Obama-era vehicle emissions standards and making the United States carbon neutral by 2050, priorities that align with the climate-centric role that Mr. Biden wants for his Transportation Department. The agency has the authority to regulate vehicle emissions, the leading source of climate-warming pollution in the United States.

Mr. Buttigieg spoke of his own “personal love of transportation ever since childhood,” and he emphasized the need to improve the country’s infrastructure, mocking Mr. Trump for repeatedly declaring an “infrastructure week” only to fail in negotiating a bipartisan deal to secure more funding to repair the nation’s crumbling roads and bridges.

“Americans expect us to see to it that the idea of an infrastructure week is associated with results and never again a media punchline,” he said.