The Senate on Thursday unanimously approved a bill to overhaul pay for law enforcement officials at Customs and Border Protection.

The Border Patrol Pay Reform Act aims to “dramatically simplify” compensation for CBP agents, including through the elimination of Administratively Uncontrollable Overtime. The Congressional Budget Office has estimated the changes would save $100 million annually.

The bill would allow Border Patrol agents to choose to work 100, 90 or 80 hours per two-week pay period. Employees who choose the 100-hour option would be paid 1.25 times their normal base pay, but would not receive any extra compensation for their overtime hours. Employees opting to work 90 hours per pay period would earn 1.125 times their normal base pay, while those who work 80 hours would simply earn their normal base pay as determined by their General Schedule rank.

Employees who work more than their agreed upon schedule -- which BP management and advocates have said occurs regularly and allows agents to remain in pursuit of criminals when their shift ends -- would be rewarded through compensatory time off. The legislation would require at least 90 percent of employees at each Border Patrol post to choose the 100-hour schedule. If a sufficient number did not volunteer for that option, the agency would force employees into it.

The bill would require CBP to make a staffing assessment at each station to determine whether a lower 100-hour requirement is appropriate moving forward.

While most employees would ultimately earn less under the revised system, the law aims to bring more stability to Border Patrol workers. Even the union that represents most of the 21,000 border agents admitted the old system -- which allowed employees to double dip into overtime -- was “bloated” and endorsed the bill as a reasonable reform.

‘‘I want to make it clear that no Border Patrol agent is happy about the prospect of losing $6,400 per year,” said Brandon Judd, president of the National Border Patrol Council, at a Senate hearing in June. “We are sacrificing a lot, but in the end, it will prove to be a boon for border security, the American public, the agency and the agents whom I represent.’’

Lawmakers began the call for changing CBP compensation after an Office of Special Counsel report found many employees were abusing overtime privileges. Legislators praised the bill’s passage as a victory for employees and good governance alike.

“By saving $100 million every year, providing Border Patrol agents with more certainty in their paychecks and work schedules, and dramatically bolstering border security, we’re delivering a win for taxpayers and a win for agents,” said Sen. Jon Tester, D-Mont., who authored the legislation.

Sen. John McCain, D-Ariz., said the increased stability would help offset the damage done by recent budget cuts.

“Spending cuts due to sequestration, coupled with an archaic and inefficient pay scale, put at risk the safety of Border Patrol agents and threaten to reverse much of the progress these agents have made along the border over the last few years,” McCain said.

CBP management also endorsed the legislation.

Border Patrol Deputy Chief Ronald Vitiello said at the June hearing the bill would create a “system that controls costs, fairly compensates certain agents for irregular and necessary work and maximizes agent capability for critical law enforcement and border security responsibilities.”

The bill would ultimately result in Border Patrol agents working an additional 2.5 million hours annually, the equivalent of adding 1,500 agents to the agency’s workforce.

Rep. Jason Chaffetz, R-Utah, who at a hearing last year said “desk jockey” CBP workers “milk the system and steal from Americans,” has introduced identical language in the House. His bill has not yet received a vote in committee.