The terms of the deal, $21 per Vanguard share, includes a 70 percent premium over Vanguard's share price at Friday's market close, The New York Times reported Monday.
Tenet also agreed to assume $2.5 billion in Vanguard's debt, the Times said.
Tenet owns 49 hospitals and 122 outpatient centers. In total, the firm operates for-profit healthcare facilities with 13,180 licensed beds.
Vanguard, based in Nashville, operated 28 hospitals with 7,081 beds. Its operations include healthcare facilities in Texas, Michigan, Arizona, Illinois and Massachusetts.
In addition, Vanguard operates four metropolitan health plans and two surgery centers, both in Orange County, Calif.
"This unique strategic transaction will bring together organizations that share a common commitment to providing high quality care and create significant new growth prospects for Tenet," said Tenet Chief Executive Officer Trevor Fetter in a statement.
"This acquisition will take Tenet into new geographic markets, expand the breadth of our service offerings, diversify our earnings sources and increase the benefits we expect to realize under healthcare reform," he said.
Investment firm Blackstone Group stands to make a significant profit on the deal, as it owns 37.9 percent of Vanguard.