Justice Stephen Breyer's majority opinion for the court held that the regulations are medically unnecessary and unconstitutionally limit a woman's right to an abortion.
Texas had argued that its 2013 law and subsequent regulations were needed to protect women's health. The rules required doctors who perform abortions to have admitting privileges at nearby hospitals and forced clinics to meet hospital-like standards for outpatient surgery.
Breyer wrote that "the surgical-center requirement, like the admitting privileges requirement, provides few, if any, health benefits for women, poses a substantial obstacle to women seeking abortions and constitutes an 'undue burden' on their constitutional right to do so."
Justices Anthony Kennedy, Ruth Bader Ginsburg, Sonia Sotomayor and Elena Kagan joined Breyer.
Chief Justice John Roberts and Justices Samuel Alito and Clarence Thomas dissented.
Thomas wrote that the decision "exemplifies the court's troubling tendency 'to bend the rules when any effort to limit abortion, or even to speak in opposition to abortion, is at issue.'" Thomas was quoting an earlier abortion dissent from Justice Antonin Scalia, who died in February.
Abortion providers said the rules would have cut the number of abortion clinics in the state by three-fourths if they had been allowed to take full effect.
When then-Gov. Rick Perry signed the law in 2013, there were about 40 clinics throughout the state. That number dropped to under 20 and would have been cut in half again if the law had taken full effect, the clinics said.
Texas is among 10 states with similar admitting privileges requirements, according to the Center for Reproductive Rights. The requirement is in effect in most of Texas, Missouri, North Dakota and Tennessee. It is on hold in Alabama, Kansas, Louisiana, Mississippi, Oklahoma and Wisconsin.
The hospital-like outpatient surgery standards are in place in Michigan, Missouri, Pennsylvania and Virginia, and it is blocked in Tennessee and Texas, according to the center, which represented the clinics in the Texas case.
Texas passed a broad bill imposing several abortion restrictions in 2013. Texas clinics sued immediately to block it claiming it impermissibly interfered with a woman's constitutional right to an abortion. The clinics won several favorable rulings in a federal district court in Texas. But each time, the New Orleans-based 5th U.S. Circuit Court of Appeals sided with the state, at first allowing challenged provisions to take effect and then upholding the law with only slight exceptions.
The Supreme Court allowed the admitting privileges requirement to take effect in most of the state, but put the surgical center provision on hold pending the court's resolution of the case.
The justices split largely along liberal-conservative lines in their emergency orders, with the court's conservative justices voting repeatedly to let the law be enforced.
Separate lawsuits are pending over admitting-privileges laws in Louisiana and Mississippi, the other states covered by the 5th circuit. The laws are on hold in both states, and a panel of federal appellate judges has concluded the Mississippi law probably is unconstitutional because it would force the only abortion clinic in the state to close.
A separate appeal is pending at the Supreme Court from Wisconsin, where federal judges have struck down that state's admitting privileges law.