The deal announced on Monday follows a series of multibillion-dollar takeovers by U.S. health insurers in their home market, including Aetna Inc's $5.6 billion buy of rival Coventry Health Care Inc and WellPoint Inc's planned $4.5 billion purchase of Amerigroup Corp .
"(Brazil's) growing economy, emerging middle class and progressive policies toward managed care make it a high- potential growth market," UnitedHealth Chief Executive Stephen Hemsley said in a statement.
U.S. health insurers have come under pressure as the government reins in reimbursement for its Medicaid and Medicare programs for the poor and the elderly and as competition grows among health plans serving employers.
The deal with Amil adds to a growing international business at UnitedHealth, the largest U.S. health insurer. The company has begun operations or struck alliances in Australia, the Middle East and the UK during the past two years.
Buying the stake in Amil gives UnitedHealth a chance to test a different model of medical service: Amil offers insurance coverage and also runs hospitals and doctor facilities. While some examples of this already exist in the United States, the largest U.S. insurance companies for the most part operate separately from networks of doctors and other healthcare providers.
"It's not something UnitedHealth has been willing to do here, but it gives them an opportunity to see how it works," said CRT Capital Group analyst Sheryl Skolnick. "Brazil is a growing economy and gives UnitedHealth more diversification."
UnitedHealth said the deal is expected to slightly increase its 2013 earnings per share.
Amil founder and Chief Executive Edson Bueno and partner Dulce Pugliese will retain the remaining 10 percent stake in the company for at least five years. Their current stake is 70 percent.
The deal includes Brazilian tax benefits worth about $600 million, bringing the effective equity purchase price to about $4.3 billion, the companies said.
UnitedHealth also said it expects third-quarter net earnings of at least $1.45 per share. Analysts on average were expecting $1.25, according to Thomson Reuters I/B/E/S.
UnitedHealth shares were off slightly at $56.85 in premarket trading, down from a Friday close at $57.13 on the New York Stock Exchange.
(Additional reporting by Esha Dey in Bangalore and Debra Sherman in Chicago; Editing by Saumyadeb Chakrabarty and John Wallace)