In 2012, after his public service ended, Mr. García Luna moved to Miami. The financial records indicated that Mr. García Luna continued to live in the United States “off the millions of dollars in bribes that the Sinaloa Cartel paid him,” the court papers said.

Prosecutors also said that when Mr. García Luna submitted an application to become a naturalized United States citizen in 2018, he “affirmatively lied about his past criminal conduct on behalf of the Sinaloa cartel.”

Mr. García Luna was expected in Federal District Court in Dallas on Tuesday afternoon for an initial appearance. His lawyer, Rose Romero, was not immediately available for comment.

Mexico’s attorney general’s office said Tuesday afternoon that it had been investigating Mr. García Luna for a range of possible crimes, including conspiracy to traffic cocaine, organized crime, making false statements and bribery. In a statement, the office said it planned to request the extradition of Mr. García Luna to Mexico.

Politically astute and well-liked in Washington, where he often met with senators and White House aides, Mr. García Luna was, at least in public, a vocal critic of corruption in Mexico. He spent much of his time in office trying to reform the Mexican federal police, increasing their salaries and firing hundreds of police commanders he did not trust.

He is considered the main architect of Mr. Calderón’s militarized approach to battling drug traffickers, which began in 2006 with the deployment of the armed forces against organized crime and the president’s official declaration of “war” on them. A cornerstone of the strategy was to focus on kingpins, on the theory that cutting off the head of a criminal organization would wither the body.

Mr. Calderón and Mr. García Luna were partly successful in that approach, capturing or killing many of the most-wanted traffickers in the country. After almost every major arrest, Mr. García Luna delighted in posing suspects alongside captured weapons and drugs in a show for the news media.