The Austin City Council unanimously approved Austin Energy’s bid to redo its residential electric rates Monday, after the city-owned utility dropped its controversial proposal to increase its base electric rate.

Under the revised rate structure, publicly released the day of the vote, all of Austin Energy’s 400,000 residential customers would see their electric bills cut — with the average customer projected to save $62 a year, utility figures show.

“This is what I consider a historic moment for us in Austin,” said Council Member Sheri Gallo, who chairs the utility’s oversight committee. “The city now has before it the opportunity to significantly address the issue of affordability in Austin with the setting of our new electric rates.”

As part of the vote, the council also signed off on the $42.5 million package of annual cuts that Austin Energy and its major customers agreed to earlier this month.

“We lowered electric rates for everyone in a way that supports conservation, cleaner air, better business practices and local control of our utility,” said Mayor Steve Adler, speaking in favor of the entire package.

The bulk of those cuts, $36.5 million, will go toward reducing electric bills for industrial and commercial customers, who had long complained that they paid some of the highest rates in the state. Major customers, such as data centers and large hospitals, will see their electric rates cut 24 percent.

Austin Energy’s major customers, including Samsung Austin Semiconductor and NXP Semiconductors, agreed not to ask the Public Utility Commission to review the rate deal. They also agreed not to ask the state Legislature to intervene in the management of the utility before 2020.

The deal included $5 million to help reduce residential electric rates. Initially the utility proposed to bump up the base rate paid by everyone, while cutting rates for those using more energy. Austin Energy scrapped that plan after finding last week that it would be a tough sell to the council members, who didn’t want to raise anyone’s rates.

The original proposal was controversial in large part because of how Austin Energy’s residential price structure works: Customers pay the base rate for their first 500 kilowatt-hours of electricity; then a second, higher rate for the next 500 kilowatt-hours; then an even higher rate for the third 500 kilowatt-hours, and so on.

Conservationists had long backed the structure, which increases the price of electricity as customers use more power, as an effective way to encourage conservation.

Utility executives, though, said it made them too dependent on selling high-priced electricity during summer heat waves to pay the bills for the entire year. They argued for increasing the base rate and decreasing the other rates as a way to cut most customers’ bills while improving the long-term financial stability of the utility.

The base rate fight quickly became a battle over who would ultimately pick up the tab: millionaires living in energy-efficient downtown condos or poor families who don’t use much electricity simply because they can’t afford it.

Data from the utility showed that during hot summer months, low-income customers in its bill discount program were more likely to end up in Austin Energy’s more expensive third and fourth use tiers than better-off customers.

However, a review of yearly data from Austin Energy by local activist Paul Robbins found that on average — over 12 months — lower income meant lower energy use.

That fight led Adler to ask the utility last week to come up with a residential rate plan that would allow it to lower all rates — which became the plan presented to the council Monday.

It wasn’t exactly what the utility was hoping for, but it’s what Austin Energy could get.

“The original proposal, in our view, strikes a balance on long-term revenue stability, and we would like to make a little more incremental progress there,” utility executive Mark Dreyfus told council members. “But given the parameters that the council discussed on Thursday (we believe) this to be the best option to meet those parameters.”