Donald Trump has named Tom Price as health secretary and reportedly plans to pick ex-Labor Secretary Elaine Chao as his transportation secretary.
Mr Price, a Georgia lawmaker, has been a vociferous critic of President Obama’s signature healthcare reforms.
Ms Chao, the wife of Senate Majority Leader Mitch McConnell, served in President George W Bush’s cabinet.
US President-elect Trump is still weighing his options in filling the posts of state, defence and treasury.
Ms Chao, who was born in Taiwan, became the first Asian-American woman to hold a position in a presidential cabinet when she led the Labor Department under President Bush from 2001-09.
The 63-year-old also served as deputy secretary of transportation and director of the Peace Corps in former President George HW Bush’s administration.
If confirmed by the Senate, Ms Chao would become the second person to hold the positions of labor secretary, transportation secretary and the spouse of a Senate majority leader.
Elizabeth Dole previously held that title.
Ms Chao will play a crucial role under Mr Trump, who has vowed to make infrastructure spending on the country’s roads, bridges and other public transit an integral part of his agenda.
She came to the US with her family at the age of eight and settled in New York, where her father became a shipping magnate.
Mr Price, a 62-year-old congressman and orthopaedic surgeon, serves as the chairman of the House of Representatives budget committee.
The Georgia congressman has fiercely opposed the Affordable Healthcare Act, considered Mr Obama’s flagship measure, and is expected to play a key role in dismantling the law.
In his campaign, Mr Trump vowed to repeal and replace the act, but has since said he favours keeping certain provisions.
Mr Trump said Mr Price was a “tireless problem solver” and “the go-to expert on healthcare policy”.
“He is exceptionally qualified to shepherd our commitment to repeal and replace Obamacare and bring affordable and accessible healthcare to every American,” Mr Trump said in a statement.
Mr Price said he was looking forward to the opportunity of serving as health secretary on behalf of the American people.
He said his aim was to create a new system that worked for patients, families and doctors, adding that it should “protect the well-being of the country while embracing its innovative spirit”.
But the appointment provoked a backlash from Democrats.
Liberal New York Mayor Bill de Blasio tweeted: “Donald Trump’s HHS pick makes it clear that he wants to take away health care from the aging and the poor. It will be up to us to stop him.”
Analysis by Anthony Zurcher, BBC North America Reporter
Donald Trump campaigned as an outsider intent on cleaning up the federal government, but his top appointments so far paint a picture of a chief executive interested in working with establishment powers to advance a traditional conservative agenda.
The president-elect’s selection of Tom Price for health and human services secretary is a perfect example, as he opted for a congressional insider with detailed knowledge of the legislative steps necessary to realise Mr Trump’s stated goal of dismantling Democratic healthcare reforms.
His pick of Seema Verma for a key healthcare agency is also illuminating. She has a track record of working within the system to advance conservative priorities. For instance, she helped prevent a grassroots Republican revolt when Indiana expanded its Medicaid insurance coverage for the poor by implementing work and eligibility requirements.
While Mr Trump blusters on Twitter and avoids most contact with the media, these latest moves seem to indicate the people running his administration will be detail-oriented and practical, albeit with a decidedly conservative bent.
The real tell, however, may be who he picks for secretary of state. If it’s Mitt Romney, the establishment insiders have prevailed. A loyalist like Rudy Giuliani? All bets are off.
On Tuesday, Mr Trump is expected to meet Mr Romney for a second time despite one of his top aides launching a public campaign against the former Massachusetts governor’s nomination.
Senior adviser Kellyanne Conway spoke out against Mr Romney on Sunday, saying Mr Trump’s supporters felt “betrayed” he would consider the 2012 Republican nominee for the prominent role.
Mr Romney was one of Mr Trump’s harshest critics during the campaign.
The president-elect will also sit down with Tennessee Senator Bob Corker, the chairman of the Senate foreign relations committee.
The two men are leading contenders for the all-important diplomatic post.
Earlier, Mr Trump met retired Gen David Petraeus. He said he was “very impressed” with the former CIA director in a tweet after their meeting on Monday.
Gen Petraeus pleaded guilty last year to mishandling classified information over documents he had shared with his biographer, with whom he was also having an affair.