• The Social Security Fairness Act passed by a vote of 76-20 in the early hours of Saturday.
• The act eliminates provisions that affect an estimated 3 million individuals.
• For retired teachers, firefighters and other state and local workers, the development caps off a decades-long battle against certain Social Security benefit reductions.

As Congress managed to avoid a government shutdown, the Senate also passed a key bill that will increase Social Security benefits for some public workers.

The Social Security Fairness Act, which passed by a vote of 76-20 in the early hours of Saturday, will eliminate Social Security provisions known as the Windfall Elimination Provision, or WEP, and Government Pension Offset, or GPO, that have been in place for decades.

The WEP reduces Social Security benefits for individuals who receive pension or disability benefits from employment where they did not pay Social Security payroll taxes. The GPO reduces Social Security for spouses, widows and widowers who also receive their own government pension income. Together, the provisions affect an estimated 3 million individuals.

The bill had enthusiastic support from organizations representing teachers, firefighters, police and other government workers who are affected by the benefit reductions.

"You shouldn't penalize people for income outside of a system when you've paid into it and earn that benefit," said John Hatton, vice president of policy and programs at the National Active and Retired Federal Employees Association, ahead of the vote. "It's been 40 years trying to get this repealed."

The bill had received overwhelming bipartisan support. The Social Security Fairness Act was passed by the House with a 327 majority in November.

The measure passed in the Senate after certain Republican lawmakers' efforts to add amendments were defeated. That included proposals to instead replace rather than fully repeal the Social Security provisions or to raise the retirement age to help offset the cost of the benefit increases.

Now the bill heads to President Joe Biden for his signature.

"Millions of retired teachers and firefighters and letter carriers and state and local workers have waited decades for this moment," Senate Majority Leader Chuck Schumer, D-New York, said after the Senate vote. "No longer will public retirees see their hard-earned Social Security benefits robbed from them, thanks to this bill."

Amendment proposed raising retirement age

The Social Security Fairness Act would cost an estimated $196 billion over 10 years, according to the Congressional Budget Office.

Those additional costs come as the trust funds Social Security relies on to help pay benefits already face looming depletion dates. Social Security's trustees have projected the program's trust fund used to pay retirement benefits may be depleted in nine years, when just 79% of benefits may be payable.

Some senators who opposed the Social Security Fairness Act had expressed concerns about the pressures the additional costs would put on the program.

Sen. Rand Paul, R-Kentucky, who earlier this week voted against moving the current version of the bill forward in the Senate, proposed an amendment to offset those costs by gradually raising the retirement age to 70 while also adjusting for life expectancy. Social Security's full retirement age — when beneficiaries receive 100% of the benefits they've earned — is currently age 67 for individuals born in 1960 or later.

"It is absurd to entertain a proposal that would make Social Security both less fair and financially weaker," Paul said at the time. "To undo the damage made by this legislation, my amendment to gradually raise the retirement age to reflect current life expectancies will strengthen Social Security by providing almost $400 billion in savings."

More from Personal Finance:
Answers to common questions on the Social Security Fairness Act
73% of workers worry Social Security won't be able to pay benefits
Early retirement is a surprise for many workers, study finds

Social Security advocacy groups have pushed for larger comprehensive Social Security reform that would use tax increases to pay for making benefits more generous.

"We want to help in making this happen, but our preference was for it to be part of a much larger Social Security reform," said Dan Adcock, director of government relations and policy at the National Committee to Preserve Social Security and Medicare, before the vote.

— CNBC's Katrina Bishop contributed to this report.