The D.C. Opportunity Scholarship, which provides low-income students with up to $12,000 for use at private schools, has been a pet project of Speaker of the House John Boehner.
Earning the seal could open the door for college scholarships, internships, and jobs that require proficiency in a second language, educators say.
Muslim families in New York City have been lobbying for the change through several administrations.
The city's education officials chose Tommy Chang, an instructional superintendent in the Los Angeles Unified School District, from a field of four finalists.
The Democrat's proposed budget would restore the estimated $1 billion in education cuts made in the previous administration, and all school districts will receive more money.
Hall, a former national superintendent of the year, was widely lauded for strong gains in Atlanta until a cheating scandal tarnished that legacy.
The district faced more than $1 billion in federal and state cuts if it did not offer the test districtwide, and the state of Illinois threatened to pull its designation as a district.
The move comes nearly two weeks after the commission approved five of 39 applications for new charter schools. The governor wanted all the applications denied.
In Sheff v. O'Neill, which was filed in 1989, the Connecticut Supreme Court ruled that the state must take action to integrate schools and reduce racial isolation.
A probe revealed that hundreds of students received credit for courses they hadn't taken or repeatedly took the same course despite passing each time.