Late last month, President Trump began grumbling — first quietly and privately, then publicly — that the Senate was moving too slowly to confirm his picks to fill highly sought ambassadorships around the world.

Mere weeks later, Senate Republicans have vastly stepped up their pace in approving his nominees, installing nearly a dozen mostly wealthy loyalists as envoys to key countries and moving more quickly than other presidents have in the past few decades.

The flurry of confirmations — 10 in Mr. Trump’s first 100 days in office — has already outpaced his most recent predecessors and that of his first term, and it comes as the president and his team have undertaken a broader effort to reshape the State Department and U.S. diplomacy. Unlike some of his cabinet nominees, most have sailed through with unanimous Republican support and at least some backing from Democrats.

That was the case on Tuesday, when the Senate voted 67 to 29 to confirm David Perdue, the former senator from Georgia and businessman, to be the U.S. ambassador to China.

His approval did not come as a surprise. Mr. Perdue maintains close relationships with many of his former colleagues and at his hearing earlier this month, he was spared critical questions on topics such as his past criticism of across-the-board tariffs or when he boasted about frequently moving American jobs overseas during his time as a business executive.

Instead, Mr. Perdue said he would dutifully carry out the president’s agenda and, like other Trump appointees to serve as top diplomats around the globe, affirmed his commitment to project an “America First” agenda while stationed abroad.

“President Trump’s America First strategy is not isolation, it’s just the reverse,” Mr. Perdue said during his hearing in early April, arguing that an intense focus on strengthening domestic manufacturing would enhance the partnership between the world’s two largest economies. “America will be a stronger ally and partner by rebuilding our strategic supply chains at home and with our friends.”

Waiting in the wings are dozens more ambassadorial nominations that the White House has sent to the Senate Foreign Relations Committee, setting the stage for what the Trump administration hopes will be a rapid transformation at the top of U.S. diplomatic ranks abroad.

Most of those confirmed so far or in line to be are extremely wealthy and politically or personally connected to Mr. Trump, such as Thomas Barrack, a billionaire private equity investor who has known Mr. Trump for decades and who was confirmed late Wednesday to serve as ambassador to Turkey. The Senate also worked late Wednesday evening, voting by an overwhelming margin to confirm Tilman Fertitta, the Texas billionaire owner of the Houston Rockets N.B.A. team, as the next U.S. ambassador to Italy.

The unusually speedy action by the Senate, usually known for its slow-moving deliberation, is a point of pride for Senator John Thune, Republican of South Dakota and the majority leader.

“We’re going to continue to confirm the president’s ambassadors as expeditiously as possible,” Mr. Thune said from the Senate floor on Monday morning as he unveiled the slate of votes to confirm several overseas posts.

Senator Jim Risch, Republican of Idaho, who leads the foreign affairs panel, said in a statement that the Senate was moving “at a record pace” to confirm Mr. Trump’s ambassadors.

The momentum began to shift after Mr. Trump expressed frustration in late March over the slow pace at which his nominees for ambassadorships were being confirmed. During a meeting at the White House with a number of unconfirmed nominees, Mr. Trump criticized the delay, prompting Senate Republicans to prioritize his ambassadorial picks over other confirmations.

“We’re being delayed as much as possible by Democrats,” Mr. Trump said during the meeting.

Although Democrats do not have enough seats to derail any of Mr. Trump’s nominees, some have sought to obstruct the process by placing holds on nominations and requiring that each post be considered and voted on individually. The move prompted Mr. Trump to lash out, accusing Senate Democrats of jeopardizing national security.

“A process that should take a matter of minutes is forced into taking months,” Mr. Trump wrote in a social media post late last month, adding that it was “so hard to watch as Highly Qualified and Respected Ambassadors, who we desperately need representing our Country in Faraway Lands, are purposefully meant to wait.”

Critics of Mr. Trump’s picks, however, argue that many are unqualified for the roles. Among them is Senator Bernie Sanders, the independent from Vermont, who has spent much of the year drawing large crowds at his “Fight the Oligarchy” tour. He pointed to the appointments of wealthy donors and billionaires as evidence of systemic corruption.

“This is just one more indication of the corruption of our campaign finance system: Billionaires not only buy elections and presidencies, they buy top jobs in the White House and important ambassadorships representing our country around the world,” he said in a statement.

Senator Brian Schatz, Democrat of Hawaii, has taken the lead in opposing State Department nominees and said he would seek procedural ways to delay each pick from moving forward, but Republicans have trudged ahead through the lengthy process anyway.

And other Democrats are not inclined to try to stand in the way. Senator Jeanne Shaheen of New Hampshire, the top Democrat on the Foreign Relations Committee, has broken with her party more than any other member of the caucus in supporting Mr. Trump’s ambassadorial picks.

Out of the 10 confirmed, she has backed eight. Two of those times she was the only Democrat supporting the nominee, though she was never the deciding vote. In an interview, she said she did not see supporting Mr. Trump’s nominees as tantamount to backing his efforts to upend American foreign policy.

“I don’t see trying to put ambassadors in positions as an effort to reshape diplomacy,” Ms. Shaheen said ahead of her vote in support of Mr. Perdue. “It is in America’s interest to have ambassadors on the ground who can defend American interests in countries around the world,” she said, adding that she had been disappointed that during the Biden administration, Senate Republicans had held up many appointments.

When asked about the approach of her Democratic colleagues who have sought to block nominations, she simply said: “Well, you have to talk to them about their views.”

Senator Chris Coons, Democrat of Delaware, a member of the foreign affairs committee who regularly meets with ambassadors, said that Mr. Trump’s picks to serve as top diplomats were not as concerning to him as other foreign policy changes Mr. Trump had instituted.

“I think the biggest impact on our standing in the world has been the crushing of U.S.A.I.D., the almost complete elimination of the significance and power of our foreign aid programs,” Mr. Coons said on Tuesday, moments before voting to confirm Mr. Perdue. “So they can prioritize confirming a few ambassadors, but it won’t change the very negative impact on our standing in the world of his recent making.”