The companies said Monday that the transaction also includes $2.5 billion in debt and value the entire deal at $4.3 billion.
Tenet will pay $21 per share, a 70 percent premium to Vanguard Health's Friday closing price of $12.37.
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Nashville, Tenn.-based Vanguard Health says its founder, Chairman and CEO Charlie Martin, will join Tenet's board.
Tenet expects annual savings of $100 million to $200 million and for the acquisition to add to earnings in the first year.
Dallas-based Tenet has secured fully committed financing for the transaction from Bank of America Merrill Lynch.
Both boards unanimously approved the deal, which is expected to close before year's end.
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