It was the first time in the nation's history that the high court had approved such sweeping public aid for a religious purpose.
The narrow ruling also is expected to give new life to President Bush's proposal to make school vouchers part of national education policy.
However, the decision drew harsh dissents, and warnings, from the court's four liberals.
The case involved a school voucher pilot program in Cleveland that a lower court had declared unconstitutional. Thursday's Supreme Court ruling reversed the lower court.
Writing for the narrow conservative majority, Chief Justice William Rehnquist said, "We believe that the program here is a program of true private choice" because parents could choose to use the vouchers to send their children to secular or religious schools.
"Any objective observer familiar with the full history and context of the Ohio program would reasonably view it as one aspect of a broader undertaking to assist poor children in failed schools," Rehnquist said later, "not as an endorsement of religious schooling in general."
The chief justice acknowledged that 82 percent of the schools participating in the Cleveland program are religious schools, "but it is also true that 81 percent of private schools in Ohio are religious schools."
Rehnquist also conceded that 96 percent of the students participating in the private school portion of the voucher program go to religious schools.
But that figure does not take into account those students who are financially helped by the program to enroll in non-traditional public schools such as magnet schools, or those who are helped by the program with tutoring in regular public schools.
Including those students bring the religious school students down to 20 percent of those being helped by the program, Rehnquist said.
"In sum, the Ohio program is entirely neutral with respect to religion," the chief justice said later in his opinion, because it allows a choice between private and public, religious and secular. "The program is therefore a program of true private choice."
O'Connor and Thomas also wrote separate concurring opinions.
Liberal Justice John Paul Stevens dissented.
Stevens asked rhetorically, "Is a law that authorizes the use of public funds to pay for the indoctrination of thousands of grammar school children in particular religious faiths a 'law respecting an establishment of religion' within the meaning of the First Amendment?"
The amendment bans such establishment, and is at the core of the American separation of church and state.
Saying the majority's ruling was "profoundly misguided," Stevens cited religious strife across the globe. "Whenever we remove a brick from the wall that designed to separate religion and government, we increase the risk of religious strife and weaken the foundation of our democracy."
Souter called the decision "potentially tragic."
In the case decided Thursday, everyone agrees that Cleveland schools were in severe crisis in the early 1990s, so much so that a federal judge placed the city's school district under the control of the state superintendent in 1995. In response, the Ohio Legislature enacted a school voucher pilot program.
Only the Cleveland area was eligible under the program's provisions.
For low-income families who chose to send their children to public schools, the program provided up to $2,250 per child. If there was money left over, higher income families were granted $1,875 per child, as long as that amount covered 75 percent of the tuition.
In the 1999-2000 school year, 56 private schools participated in the program; 46, or 82 percent, were religious schools. Of the 3,700 students participating in the program that school year, 96 percent attended religious schools.
Several parents and public school students filed suit against the Ohio program, saying it violated the First Amendment's ban on the establishment of religion.
A federal judge issued a preliminary injunction against the implementation of the program, but that order was eventually stayed by the Supreme Court.
The judge then ruled for the challengers. A federal appeals court upheld the judge, pointing out that the program mainly helped students attend religious schools, and that the restrictions on funding basically made religious schools the only type of private institutions that could afford to participate.
Cleveland then asked the Supreme Court for review. After hearing argument in February, the narrow Supreme Court majority sided with Ohio officials Thursday.
The majority decision reverses the appeals court.
(Nos. 00-1751; 00-1777 and 00-1779, Zelman vs. Harris etc.)