Behind a Texas law that has confounded legal scholars and given abortion opponents hope is a publicity-shy, 45-year-old West Coast litigator known for his command of abstruse legal theory.

The Texas Heartbeat Act has survived a brush with the Supreme Court and made Texas the most restrictive in the nation for abortion access, thanks largely to its unusual enforcement scheme. The law puts ordinary Texans—not any government official—in charge of enforcing a prohibition on performing or aiding abortions after six weeks of pregnancy, making it more difficult to challenge in court.

The principal architect of the private-enforcement provision is Jonathan F. Mitchell, a constitutional litigator, former Justice Antonin Scalia clerk and law professor who in his spare time works pro bono advising the Republican legislators in Texas, according to people familiar with the legislation’s development. He is active with the Federalist Society, the conservative legal group.

Mr. Mitchell helped draft the bill at the suggestion of state Sen. Bryan Hughes, an East Texas Republican, who said he sponsored it as a way for Texas to enact a so-called heartbeat bill that many other states passed into law.

But the senator said he also wanted to avoid the fate of those other bills, which were all struck down by judges who said the laws placed an undue burden on women seeking an abortion before the fetus was viable. District attorneys in Texas’ more liberal cities were already saying they wouldn’t enforce abortion bans in the event of a Supreme Court ruling overturning Roe v. Wade. So Mr. Hughes wanted a bill that could remain effective even without prosecutions.

Texas state Rep. Shelby Slawson stood with co-sponsors of the legislation at the Capitol in May answering questions.

Photo: Eric Gay/Associated Press

“We knew we had to have another way,” said Mr. Hughes, chairman of the chamber’s influential Senate State Affairs policy-making committee. “We were going to find a way to pass a heartbeat bill that was going to be upheld.”

Some legal scholars, including conservatives, are dubious that the Texas law can survive a more sustained legal review and expect courts—either at the federal or state level—to halt it with some kind of general injunction. But they say Mr. Mitchell still has defied the odds by seeing the law go into effect.

“He would have been a pretty successful legal academic,” said Ilya Somin, a George Mason University law professor and former colleague of Mr. Mitchell’s. “He’s a creative legal thinker.”

Mr. Mitchell has taught law at several law schools, including George Mason University and Stanford Law School, before entering state government in 2010 as the Texas’ solicitor general under Gov. Rick Perry. He left the job when Mr. Perry’s tenure ended. In 2017, President Donald Trump said he would tap Mr. Mitchell to lead the Administrative Conference of the United States, an obscure federal agency that advises on administrative law and regulatory procedures. But his confirmation never came up for a vote.

In 2018, Mr. Mitchell drafted “The Writ-of-Erasure Fallacy,” a Virginia Law Review article that articulated the legal theories that would eventually find their way into the Texas abortion law. The article was a deep dive into the subject of judicial review and raised the idea that when a court rules a statute unconstitutional, the law isn’t erased from the books and could be modified to allow for “private enforcement.”

He described how laws could be constructed to “enable private litigants to enforce a statute even after a federal district court has enjoined the executive from enforcing it,” without going in-depth about the applicability to abortion laws.

After opening a solo law practice, Mr. Mitchell extended the idea to abortion in 2019 when he advised an antiabortion East Texas pastor in drafting an ordinance adopted by a number of smaller Texas cities, including the city of Lubbock, that allowed Texas citizens to obtain an injunction against anyone performing or helping to carry out an abortion. Efforts by abortion-rights advocates to stop enforcement of the Lubbock ordinance failed in federal court, where a judge ruled that the plaintiff, Planned Parenthood, couldn’t sue the government over the law.

The Texas Heartbeat Act, or SB 8, as the Texas law is known, is a legal labyrinth of statutory construction that has confounded some of the legal profession’s most seasoned minds. Abortion-rights activists have denounced the law as diabolical, while some legal scholars have marveled at its creative clauses.

In a typical challenge to an antiabortion law, abortion-rights advocates can sue government officials tasked with enforcing the statute and wage their fights in courts and regions of their choosing. SB 8, which many Republican lawyers in the statehouse helped shape into its final form, turns the table on the geographic advantage. Claimants can sue on their home turf, even if the abortion-provider defendant is located elsewhere, and avoid courts in more Democratic areas. With no government official to sue, plaintiffs lack standing to move pre-emptively against the laws.

The law brims with financial enticements for claimants and their lawyers. The law sets a floor for damages at $10,000 per unlawful abortion but sets no limit on how much money claimants can recover. If they prevail, they can also demand the losing party pay their legal bills. If they lose in court and their case is dismissed, they owe the defendant nothing.

The law permits multiple lawsuits to be filed by different individuals over a single abortion. Once a claimant collects damages, though, the others suing may not collect more money from the same defendant for the same violation.

The Republican-led state Senate and House passed the measure in May with votes almost entirely split along party lines. Between the two chambers, only two Democrats voted for the bill. No Republicans voted against the ban. Texas Gov. Greg Abbott, a Republican, signed the bill on May 19, and it went into effect Wednesday.

In an unsigned 5-4 order, the Supreme Court declined to block the law from taking effect. The conservative majority wrote that there were “serious questions regarding the constitutionality of the Texas law” but said the court might lack the jurisdiction to act because of procedural technicalities. The three liberal justices and Chief Justice John Roberts filed dissents.

Write to Jacob Gershman at jacob.gershman@wsj.com