General Electric reached a deal to combine its oil-and-gas business with Baker Hughes, creating an energy powerhouse that would give GE a cost-effective way to play any recovery in the industry.

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GE will contribute its oil-and-gas business and $7.4 billion in a special cash dividend to the new entity, which will have publicly traded shares and be 62.5% owned by GE and 37.5% owned by existing Baker Hughes shareholders.

The Wall Street Journal reported last week that the companies were in talks about a potential transaction.

A combination creates a company with more than $32 billion in revenue that could cut costs to better compete with rivals such as Schlumberger Ltd. to provide equipment and services to oil rigs and wells. It would enable GE to benefit from an expected recovery in the industry without having to pay for a full acquisition of Baker Hughes. It would also enable the companies and their shareholders to benefit from cost and other synergies from putting the two businesses together.

After two brutal years, GE and some of its rivals in the oil-and-gas business have begun to see signs of hope. Crude prices, which plunged to $30 a barrel this year from more than $100 in 2014, have rebounded to around $50 recently.

--Ted Mann and Austen Hufford contributed to this article.

Write to Dana Cimilluca at dana.cimilluca@wsj.com, Dana Mattioli at dana.mattioli@wsj.com and David Benoit at david.benoit@wsj.com