In the end, he said the process meant “perfectly legal naturalized Americans were burdened with what the Court finds to be ham-handed and threatening correspondence from the state which did not politely ask for information but rather exemplifies the power of government to strike fear and anxiety and to intimidate the least powerful among us.”

The judge also said that evidence presented in the case showed “no widespread voter fraud,” which he described as an “infinitesimal” problem.

The lists released in January were based on data from the Department of Public Safety, which is responsible for law enforcement, vehicle registration and the issuance of driver’s licenses, akin to the Department of Motor Vehicles in other states.

Andre Segura, the legal director for the American Civil Liberties Union of Texas, which filed one of the lawsuits that is to be settled, said the voter review had been based on a backward-looking process.

If someone identified as a noncitizen when applying for a driver’s license, for example, and then registered to vote at a later date, the process made no allowance for the possibility that the person had become a citizen in the intervening months or years, he said.

“We know that tens of thousands of people naturalize each year,” Mr. Segura said. “What we argued is that this proves the process was essentially designed to target naturalized citizens.”

The Texas Secretary of State’s office said the new process would flag only people who registered to vote and then later identified themselves as noncitizens to the Department of Public Safety when they applied for a driver’s license or a personal identification card.