The acquisition will position the companies for future growth as they prepare for the launch of insurance exchanges, they said.
The deal comes on the heels of the US Supreme Court's decision in late June to uphold President Barack Obama's health care reform, the Affordable Care Act.
Under the overhaul, states are to have health insurance exchanges, where consumers can shop for coverage, starting in 2014.
WellPoint will pay $92 a share in the all-cash deal for Amerigroup, which specializes in federal and state health care programs such as Medicaid, serving the poor and disadvantaged.
The share price represents a 43 percent premium over Amerigroup's closing price Friday. WellPoint will pay about $4.4 billion for the shares and assume Amerigroup's debt.
"We believe that this combination will create an industry leader in the government sector serving Medicaid and Medicare enrollees," WellPoint's chief executive Angela Braly said in a statement.
The companies said the combination was aimed at "creating better health care quality at more affordable prices for their customers."
The transaction was expected to close in early 2013.
"Upon completion, WellPoint, with its affiliated Medicaid plans, will serve more than four-and-a-half million beneficiaries of state sponsored health care programs. The combined company's Medicaid footprint will include 19 states," the companies said.
WellPoint, based in Indianapolis, Indiana, has about 96 million people in its health plans.
Amerigroup currently serves about 2.7 million members in 13 states.
Investors applauded the deal in early New York trade. Amerigroup shares soared 37.9 percent to $88.72, while WellPoint climbed nearly 3.0 percent to $61.69.