The offer values Lufkin at $88.50 per share, representing a premium of 38 percent to the stock's Friday close.
Lufkin, which makes artificial lift technologies and industrial equipment, has operations in the U.S., Canada, Latin America, the Middle East, and Europe.
Artificial lift refers to the use of external means to increase the flow of liquids such as crude oil or water from a production well.
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GE has been boosting its presence in the energy sector with purchases of oilfield equipment maker Dresser, John Wood's well support division, and British oil equipment company Wellstream.
Oil and gas business contributed about 10 percent to GE's total revenue last year.
Shares of Lufkin surged more than 35 percent in pre-market trading, while shares of GE also traded higher.
image: © Valerie Everett