Tenet will pay $21 per share, a 70 percent premium to Vanguard Health's Friday closing price of $12.37.
Shares of Vanguard Health soared $8.14, or 65.8 percent, to $20.51 in premarket trading Monday.
The companies said Monday that the transaction also includes $2.5 billion in debt and value the entire deal at $4.3 billion.
Following the acquisition, Tenet will own 79 hospitals and 157 outpatient facilities. It currently has 49 hospitals and 126 outpatient facilities.
Both boards unanimously approved the deal, which is expected to close before year's end
Tenet expects annual savings of $100 million to $200 million and for the acquisition to add to earnings in the first year.
Nashville, Tenn.-based Vanguard Health said that its founder, Chairman and CEO Charlie Martin, will join Tenet's board. Vanguard's vice chairman, Keith Pitts, will continue in that position at Tenet.
Dallas-based Tenet has secured fully committed financing for the transaction from Bank of America Merrill Lynch.