Aetna Inc., the third-biggest U.S. health care insurer, has agreed to buy Coventry Health Care Inc. for about $5.6 billion to increase its share of government business following President Barack Obama’s health-care overhaul.

Aetna joins competitors WellPoint Inc. and Cigna Corp. in making acquisitions as the U.S. government expands medical coverage. Indianapolis-based WellPoint said last month it would buy Medicaid insurer Amerigroup Corp. for $4.9 billion, and Cigna bought Medicare specialist Healthspring Inc. for $3.8 billion in January. Aetna Chief Financial Officer Joseph Zubretsky said in an interview last month that he was open to an acquisition of any size as long as it’s a “strategic fit.”

Aetna will pay $42.08 a share for Bethesda, Md.-based Coventry, including $27.30 in cash and 0.3885 Aetna share, the companies said Monday in a prepared statement. That represents a 20-percent premium over Coventry’s closing price of $34.94 on Aug. 17, which gave the company a market value of $4.68 billion. Including debt, the deal is valued at $7.3 billion.

The purchase will increase Aetna’s share of business from government health plans including Medicare and Medicaid to more than 30 percent from 23 percent, the companies said. Coventry will add more than 5 million customers to Hartford, Conn.-based Aetna’s 36.7 million members, including 1.5 million people on the drug plans of Medicare, the program for the elderly and disabled.

“It’s a deal that almost had to happen,” said Thomas Carroll, a Stifel Nicolaus & Co. analyst in Baltimore. “For Aetna to really compete effectively amongst the other large national managed care companies, they have to do more in terms of gaining market share in the commercial business as well as getting a bigger foothold in Medicare and Medicaid, which are the growth areas in managed care over the next decade.”

Aetna said it will finance the purchase with a combination of cash on hand and about $2.5 billion in new debt and commercial paper. The deal is expected to close in the middle of next year, the companies said.

The acquisition would be the largest by value for a health insurer in the past five years. There have been 119 acquisitions of health-maintenance organizations in that period, with an average size of $646.6 million and an average premium of 30 percent, according to data compiled by Bloomberg.

The Coventry acquisition will add to Aetna’s operating earnings per share next year, and will add 45 cents a share in 2014 and 90 cents the following year, excluding transaction and integration costs, the companies said.

The deal also will expand Aetna’s reach among small businesses and customers who buy coverage on their own instead of through an employer, Mark Bertolini, Aetna’s CEO, said on a conference call with analysts today. Both markets are expected to expand under the health-care overhaul.

“Coventry’s historical strength with small businesses and individuals will balance Aetna’s strength” with big employers, the CEO said.

WellPoint, the second-largest U.S. health plan, paid a 43-percent premium to Amerigroup’s previous closing price, while Cigna paid a 37-percent premium for Healthspring.

Obama’s health-care law seeks to add as many as 17 million patients under Medicaid, the insurance program for the poor, while individual states have increasingly turned to insurers to help them manage existing programs at lower costs. Medicare managed-care plans are among the fastest-growing products for health insurers as Americans age.