The Obamacare critic Azar, 50, had until last January served as president of Lilly USA, the American arm of drug giant Eli Lilly and Company.
The Yale Law graduate Azar also had served as general counsel and then as deputy secretary of HHS in the administration of President George W. Bush.
If his nomination is approved, Azar would replace Trump's first HHS chief, Dr. Tom Price, who resigned detailed his use of private, pricey charter jets and government planes instead of flying commercial on department business.
Azar's prospective department has the biggest budget of any single agency in the federal government — more than $1 trillion.
HHS oversees the sprawling Medicare and Medicaid programs, which together proved health insurance coverage to almost 130 million Americans.
HHS is also resonsible for overseeing the Affordable Care Act, popularly known as Obamacare.
Government-run ACA exchanges sell private health insurance plans to more than 10 million people, and the law also expanded Medicaid coverage to more than 10 million other people.
Azar in February, during an interview on CNBC in February, said "The remarkable thing here is Obamacare is failing completely on its own terms."
Speaking about what was then a prospective Republican Obamacare repeal-and-replacement bill, Azar said there was a consensus among Republicans and Democrats that the government should play a role in expanding insurance coverage and subsidizing its purchase by individuals. But he suggested that the way to do that was one other than Obamacare's system.
And Azar was firm in his prediction that the GOP bill would become law within months.
"There will be a piece of legislation passes this year that is called 'the repeal of Obamacare,' " Azar said. "I don't know what's going to be in the substance of it, but there will be a piece of legislation that says that."
Azar was wrong about that. Republican leaders in Congress repeatedly fail to pass repeal-and-replace bills, despite controlling both the Senate and the House.
Azar has previously said he does not believe the expansion of Medicaid has been successful, saying he would have preferred to use government money through "private-sector vehicles" to deliver health care.
Sen. Lamar Alexander, R-Tenn., chairman of the Senate Health Committee, said, "As a former Deputy Secretary of Health andHuman Services and private sector executive, Alex Azar has the qualifications and experience to get results."
"The Senate Health Committee will promptly schedule a hearing on his nomination," Alexander said.
Sen. Ron Wyden, D-Ore., the ranking Democrat on the Finance Committee, said "I will closely scrutinize Mr. Azar's record and ask for his commitment to faithfully implement the Affordable Care Act and take decisive, meaningful action to curtail the runaway train of prescription drug costs."
"Health care is too personal to be driven by politics, but that is what the leadership of HHS has offered so far," Wyden said.
Wyden also said, "The Trump administration's track record on health care to date is objectively abysmal. At every turn, the president has broken his promises to American families to lower health care costs, expand access, and bring down the high price of prescription drugs."
Brad Woodhouse, director of the Protect Our Care Campaign, an Obamacare defense group, blasted Azar's selection.
"President Trump has nominated in Mr. Azar someone who shares his misguided and factually flawed views on the Affordable Care Act," Woohouse said. said Woodhouse.
"Mr. Azar, a drug industry lobbyist, has been a harsh critic of the ACA and has gone so far as to say that the law is 'circling the drain' despite evidence to the contrary. In fact, the ACA is working despite President Trump and former HHS Secretary Tom Price's repeated efforts to repeal and sabotage it — open enrollment is off to a strong start, plans remain affordable and every county in the country is covered."