In an interview on Thursday, the governor’s counsel, Alphonso David, outlined the major changes that will be made to the bill, including a shift in who picks the commission’s 11 members. Under the bill, as originally written, the Legislature would have named six members, a potential voting majority; the judiciary would appoint three; and the governor’s office would tap two members. That was amended so that the governor now will have a greater say in the commission’s makeup, with four members, the same as the Legislature. The judiciary will still name three members, but the appointees must be retired judges, Mr. David said.

The commission’s findings will be issued through the appellate courts, not the Court of Appeals, Mr. David said, sidestepping concerns about an improper expansion of the court’s judicial power. Finally, the amended version will prevent the commission from “investigating investigations,” or examining ongoing cases in which no charges have been filed.

Having four members from the governor’s office may raise some eyebrows, considering Mr. Cuomo’s well-established reputation for maximizing his influence. But the governor’s office said that change was made to mirror the makeup of the state Commission on Judicial Conduct, which investigates complaints against judges.

The commission was applauded by groups like the Legal Aid Society, which called it “a crucial step toward avoiding wrongful incarceration and a way to help prevent future misconduct.”

That sort of declaration was echoed in a news release from the governor’s office that said the commission could potentially fight “malicious prosecutions and wrongful convictions,” which frequently impact “people of color and marginalized communities.” Indeed, before Monday’s deadline to sign or veto the bill, Mr. Cuomo’s primary opponent, Cynthia Nixon, had been calling on him to approve it, accusing him of “dragging his feet” because of fear of “powerful prosecutors in the New York establishment.”

Dani Lever, the governor’s press secretary, scoffed at that assertion.

“We know that Ms. Nixon is new to the legislative process, so we’re happy to explain,” Ms. Lever said. “The Legislature controls the timing of when a bill is sent to the governor.”

For his part, Mr. DeFrancisco, who is retiring from the Senate at the end of this year, was not available on Thursday to comment about the proposed changes; his office said he was traveling. A defense lawyer by trade, Mr. DeFrancisco has previously expressed shock at bad prosecutions, including a 2016 trial in St. Lawrence County in which a black soccer coach was accused of killing a 12-year-old white boy, with little hard evidence. The coach, Oral Nicholas Hillary, was eventually acquitted.