AMC will pay $30 per share in cash to buy all of Carmike's outstanding shares, which represents a premium of about 19.5 percent to Carmike's Thursday's close.
Chinese property and investment firm Dalian Wanda Group had acquired AMC Entertainment for $2.6 billion in 2012.
The transaction will be funded through a combination of existing liquidity, including cash on hand, and incremental debt. The debt financing commitment is being provided by Citigroup Global Markets Inc.
Dalian Wanda Group also agreed to acquire a majority stake in Legendary Entertainment earlier this year, valuing the U.S. movie studio company at between $3 billion and $4 billion.
AMC, the second-largest movie theater chain in North America, currently has 387 locations and 5,426 screens while Carmike has 276 theaters with 2,954 screens in 41 states.