General Electric Co. is nearing a roughly $30 billion deal to combine its oil-and-gas business with Baker Hughes Inc., creating an energy powerhouse that would give GE a cost-effective way to play any recovery in the industry.

GE plans to contribute its oil-and-gas business and some cash to the new entity, which would have publicly traded shares and be majority-owned and controlled by GE, people familiar with the matter said. The transaction is to be announced Monday morning, the people said.

Exact...