General Electric Co. said Thursday it was cutting 12,000 jobs in its power business, or nearly 18% of the unit’s workforce, as the conglomerate slashes costs and battles overcapacity in an industry in upheaval.

GE’s Power unit has been a drag on earnings for the struggling company as global demand has dropped in tandem with GE integrating its acquisition of power assets from France’s Alstom SA . GE has said it misjudged the market as volume dropped in traditional coal and gas-fired power, while renewable energy sources grew.

The shrinking of the power business is part of a broader reorganization at GE under new Chief Executive John Flannery, who last month cut the once-sacred dividend in half and sharply lowered profit targets.

The power business, which makes turbines for coal and gas-fired power plants, is one of the 125-year-old company’s original businesses and produces a third of the world’s electricity. It is GE’s largest by both revenue and number of employees. It generated about $27 billion in revenue last year and employed 57,000 at the start of the year. But it has been revamped since then, merging with GE’s Energy Connections division and selling water assets and other operations.

Its biggest rival, Siemens AG SIEGY -1.24% , said last month it would cut about 6,900 jobs to combat weak demand.

Former CEO Jeff Immelt expanded GE’s power business through acquisitions, including the 2015 purchase of assets from Alstom. The deal was a big bet on coal-fueled power, nearly doubling GE’s fleet of large turbines in coal plants to more than 1,500 world-wide. But industry preferences were changing, with the growth in electricity generation shifting toward wind and solar, technologies that don’t rely on the large turbines manufactured by GE.

“This decision was painful but necessary for GE Power to respond to the disruption in the power market, which is driving significantly lower volumes in products and services,” GE Power Chief Executive Russell Stokes said in prepared remarks. He said the company anticipates those challenges continuing.

Mr. Flannery, who took over in August, is focusing on GE’s power, aviation and health-care divisions as he implements a sweeping turnaround effort at the 125-year-old conglomerate. At the end of 2016, GE had around 295,000 employees.

In a presentation last month, Mr. Flannery highlighted GE’s mistakes in the power business, saying it was a tough market “and we have exacerbated the market situation with some really poor execution. It’s fixable.”

Executives warned then that the business was sitting on too much unsold inventory and that its operating profits would fall 20% this year and another 25% in 2018. They also pledged to reduce costs and shrink its factory footprint.

Beyond the broader market challenges, GE didn’t move quickly enough to make cuts and other changes on top of its effort to integrate the Alstom assets, people at the company and industry observers say. Mr. Flannery also has said the deal was overpriced and was hurt by its delayed closing.

The deal was met with opposition in France and involved a long review process and negotiations to win political support. GE also had to outmaneuver German and Japanese rivals, and agreed to create jobs in France.

The job cuts will happen over the next 18 months with about half of them in Europe, where the power business has large factories in France, Germany and Switzerland, according to a person familiar with the matter. The company still expects to meet its obligations to the French government under the Alstom deal, which included a promise to create 1,000 high-skilled jobs by the end of 2018, the person said.

The unit has 153 manufacturing, repair and service sites around the globe. Two of its biggest U.S. facilities are in Schenectady, N.Y., and Greenville, S.C. Several hundred workers at those sites have been notified of layoffs, the person said.

“We are not certain these efforts will be enough to turn around Power,” said Jim Corridore, an analyst with CFRA Research. He said the power sector pressures are real but GE made it worse with poor execution and by consistently telling investors that things would get better.

“GE made promise after promise,” he said. “There was always a reason for why there was no reason worry.”

The layoffs are in addition to 6,500 job cuts, mostly in Europe, that GE Power announced in early 2016 shortly after the Alston purchase closed.

The Paris-based International Energy Agency predicts that renewable energy’s global share of power will rise from 24% to 40% by 2040. This trend can be seen in emerging economies, such as India, where coal’s share of power generation is expected to drop from 76% to about 50%, while wind and solar power rise dramatically.

The shift is proving brutal for companies like GE and Siemens that manufacture equipment at the heart of coal plants and gas-fired combined-cycle power plants. Solar-panel manufacturing is dominated by Chinese companies. GE has a significant presence in wind turbines, but the market is spread among several companies.

Siemens said last month that demand for gas turbines that generate more than 100 megawatts has fallen to about 110 turbines a year, compared with world-wide production capacity for Siemens and its competitors of some 400 of these turbines a year.

“The power-generation industry is experiencing disruption of unprecedented scope and speed,” Lisa Davis, a Siemens board member with special oversight of the power-and-gas division, said last month.

What’s more, wind and solar generation equipment tends to be less complex and requires fewer workers to manufacture, according to industry experts.

GE has a renewable energy business, which mostly manufactures wind turbines and which Mr. Immelt built up through acquisitions. It had revenue of about $9 billion last year and employed 12,000 people at the start of 2016. Last month, Mr. Flannery said the renewables market was growing but there was intense price competition hurting profits.

The problems at GE go beyond its power business, though Mr. Flannery has blamed its woes for much of the sudden deterioration of the company’s performance. The longtime head of the unit, Steve Bolze, left the company in June and was replaced by Mr. Stokes, a 20-year GE veteran who previously ran its Energy Connections unit.

GE is hoping to cut $3.5 billion in structural costs this year and next. Mr. Flannery also wanted to step back from certain businesses, like GE Lighting and its transportation division. GE shares gained 1.4% in Thursday trading. Year to date, the company’s shares are down about 44%.

Mr. Flannery also is remaking the GE board by reducing its size and pushing for new voices. He has specifically highlighted the need from someone with expertise in the power industry or from a utility.

—Allison Prang and Russell Gold contributed to this article

Write to Thomas Gryta at thomas.gryta@wsj.com