President Trump announced Friday that the Education Department would no longer manage the nation’s $1.6 trillion student loan portfolio or supervise “special needs” programs in a major shake-up of an agency he has sought to eliminate.

Student loans will move under the Small Business Administration, while special education services, along with nutrition programs, will move under the Department of Health and Human Services, Mr. Trump said.

Mr. Trump told reporters gathered in the Oval Office that the moves would take place “immediately,” adding that he believed the restructuring — which critics swiftly vowed to challenge in court — would “work out very well.”

“They’ll be serviced much better than it has in the past. It’s been a mess,” he said of the loans. He added, “You’re going to have great education, much better than it is now, at half the cost.”

Mr. Trump laid the groundwork for his announcement on Thursday, with an executive order aimed at closing the Education Department. The department cannot be closed without the approval of Congress, which created it. But since Mr. Trump took office, his administration has slashed the department’s work force by more than half and eliminated $600 million in grants.

Reassigning such primary functions would further hollow out the agency, though education experts and union officials questioned Mr. Trump’s authority to do so unilaterally, particularly in the case of student loans. Many suggested that the result would not be better service — only more confusion for borrowers.

Karoline Leavitt, the White House press secretary, insisted on Thursday that major programs like student loans would still be run out of the Education Department, albeit a much leaner one. Pressed Friday to clarify what functions would be moved, and what legal authority Mr. Trump had to transfer them, she invoked Congress.

“President Trump is doing everything within his executive authority to dismantle the Department of Education and return education back to the states while safeguarding critical functions for students and families such as student loans, special needs programs and nutrition programs,” she said. “The president has always said Congress has a role to play in this effort, and we expect them to help the president deliver.”

High ranking Republicans in Congress have already committed to introducing legislation to support Mr. Trump’s efforts to eliminate the Education Department.

Beth Maglione, the interim president and chief executive of the National Association of Student Financial Aid Administrators, said it was “unclear” whether Mr. Trump could move aid programs away from the department. She suggested that a transition, even one authorized by Congress, would require time and careful planning.

“The administration would first need to articulate a definitive strategy outlining how the work of administering student aid programs would be allocated within the S.B.A., determine the necessary staffing and resources and build the requisite infrastructure to facilitate the transition of these programs to another federal agency,” she said. “In the absence of any comprehensive plan, a serious concern remains: How will this restructuring be executed without disruption to students and institutions?”

In the executive order, the president compared the size of the federal student loan portfolio with that of Wells Fargo, the bank — noting that Wells Fargo had over 200,000 employees, while only 1,500 people worked in the Education Department’s Office of Federal Student Aid.

“The Department of Education is not a bank, and it must return bank functions to an entity equipped to serve America’s students,” the order stated.

On Thursday, Mr. Trump pledged that the legally mandated funding for students who attend high-poverty schools and who rely on federal Pell grants, as well as “resources for children with special disabilities and special needs​,” would be preserved even as the department was gutted in accordance with his plans.

He indicated that this was important to Linda McMahon, Mr. Trump’s education secretary, who served as S.B.A. administrator during his first term.

The restructuring Mr. Trump announced on Friday would transfer some of the largest programs handled by the Education Department into agencies that have had minimal involvement with schools and are going through staffing reductions themselves.

The S.B.A., headed by Kelly Loeffler, announced Thursday that it would cut 43 percent of its roughly 6,500 workers, while H.H.S., led by Robert F. Kennedy Jr., has offered buyouts to most of its roughly 80,000 employees.