President Andrés Manuel López Obrador of Mexico leaves office at the end of September. But before he does, he will see one of his final missions largely fulfilled: a sweeping redesign of the judiciary that he says is needed to fight corruption.

The changes championed by the president would shift the judiciary from an appointment-based system largely grounded in training and qualifications to one where voters elect judges and there are few requirements to run. Nearly all of Mexico’s more than 7,000 judges could be affected by the measure, making the overhaul one of the most sweeping of its kind attempted anywhere in the world in recent decades, according to legal scholars.

The changes would apply to the 11 justices currently on the Supreme Court; 1,635 federal judges and magistrates; and more than 5,700 judges at the state and local level. Long lists of requirements to become a judge would be eliminated, especially at the federal level, opening the way for people who simply have a law degree and a few years of legal experience to run.

The measure was approved in the lower house of Congress last week, and it overcame its biggest obstacle when it was narrowly passed in the Senate on Wednesday — even after protesters barged into the building and interrupted the session on Tuesday. It will now go to Mexico’s state legislatures, where it is expected to easily pass in the coming months.

The proposed measure could produce one of the most far-reaching judicial overhauls of any major democracy. Relatively few countries allow judges to be elected on a significant scale, but none to the degree that Mr. López Obrador is proposing, according to legal scholars.

The government says the measure is needed to modernize the judiciary and instill trust in a system plagued by graft, influence-peddling and nepotism. Mr. López Obrador’s successor, Claudia Sheinbaum, takes office on Oct. 1 and has fully backed the plan.