Koch Industries, which owns brands such as Brawny paper towels, Dixie Cups and Lycra, is controlled by Charles and David Koch, two of the world's richest men.
The deal, pitched at $38.50 per share, represents a 42 percent premium on average to the Friday closing prices of Molex's two classes of publicly traded shares, the companies said on Monday.
The deal has the support of the founding Krehbiel family and key executives who control about a third of the company's common stock and 94 percent of the 94,255 unlisted Class B common shares. The Class B stock, held by 13 individuals as of June 30, is critical for approval of any deal.
Frederick Krehbiel and John Krehbiel Jr. are joint chairmen of the Molex board and are former CEOs of the 75-year-old company, which is run out of Lisle, Illinois.
Holders of Molex's 95.6 million common shares will get a premium of 31 percent to the stock's Friday close, while holders of 82.5 million Class A shares will get a premium of 56 percent.
Molex will become a standalone unit of Koch Industries, which is the second-largest private company in the United States according to Forbes, with estimated annual sales of $115 billion.
Koch Industries Chief Executive Charles Koch said Molex would fit well with his company's culture and core capabilities and would provide a significant new platform for growth.
Molex will continue to be run by its current management.
UBS analysts expressed surprise at both the healthy valuation of the deal and the buyer.
"The precise motivation of the acquisition is unclear to us at this juncture," Amitabh Passi and James Hillier said in a note.
"We expect the take-out of (Molex) to be generally positive for larger peers, TE Connectivity Ltd and Amphenol Corp, given prospects for industry consolidation at reasonably healthy multiples and a more concentrated competitive landscape," they said.
Amphenol shares were up 1.5 percent at $76.11, while shares of TE Connectivity were up 1.5 percent at $50.99 in late morning trade on the New York Stock Exchange.
William Blair & Co and BDT & Co are financial advisers to Molex, while Goldman, Sachs & Co provided a fairness opinion and other financial advice, the companies said.
Koch is represented by Latham & Watkins LLP.
Molex's common stock rose to $38.55 in morning trading on the Nasdaq, its highest price since 2006, while the Class A stock rose to $38.32, its highest since 2000.
The Koch brothers, known for their conservative views, walked away from talks to buy the Tribune Co's newspaper assets late last month, concluding that the papers were not economically viable.
(Reporting by Bijoy Koyitty in Bangalore; Editing by Maju Samuel and Ted Kerr)