Zurich-based ABB sees potential for annual cost benefits of $200 million with the deal, which includes an agreement for long-term use of GE's brand and a strategic partnership. In 2016, the GE business had sales of $2.7 billion.
The GE products include circuit breakers, switchgear, components for lighting control and power supply equipment for facilities including data centres. ABB's portfolio includes similar products.
ABB is seeking to better penetrate the North American market and gain access to GE's larger installed base of electrical installations worldwide.
ABB said the business had been "an unloved child" and pledged to upgrade aging products with its own technology to help arrest a declining U.S. market share.
ABB is suspending its $3 billion share buyback programme as part of the deal, which will bolster its position as the second-biggest supplier of electrical components behind France's Schneider Electric.
ABB is also wagering on being able to cut costs and boost profitability at the Georgia-based GE unit.
"The key rationale of the integration is, first we will make this business better. And then afterwards, we will make this business bigger and better," said ABB Chief Executive Ulrich Spiesshofer.
ABB expects integration costs of $400 million.
The GE unit's operating earnings before interest, taxes and amortisation (EBITA) are just 6 percent of sales, less than half the 15 percent operating margin at ABB's comparable Electrification Products division.
"Without that, the economics wouldn't have worked," he told reporters on a call. "With the supply partnership, the economics at the price of 0.9 times revenue is working."
GE has been under pressure from activist investor Nelson Peltz's Trian Fund Management to sell assets and focus on higher-margin businesses.
Some analysts said the price was surprisingly high given the GE business's low profitability.
"GE Industrial Solutions isn't in top shape, so ABB has its work cut out for it," said Zuercher Kantonalbank analyst Richard Frei.
ABB said it would finance the deal -- likely its last for some time -- with cash and did not need to raise equity capital. Its shares were little changed in early trading.
GE had resumed negotiations to sell the business to ABB after moderating its price expectations, people familiar with the matter told Reuters in August.
Credit Suisse and Dyal Co acted as financial advisers to ABB, and Davis Polk & Wardwell provided legal counsel.