The purchase will transform the two regional players into a cinema operator with a national footprint, AMC CEO Adam Aron told CNBC's "Squawk on the Street" on Friday.
Carmike tends to serve smaller cities in the South and Southeast, while AMC is concentrated in large cities, primarily in the Northeast, Midwest and West, he said.
Share prices of Carmike jumped more than 16 percent in trading following the announcement. AMC's stock was up more than 2 percent.
Aron said he believes the deal will close by the end of the year, positioning AMC to capture momentum at the box office and take advantage of a strong slate of movies in 2017 and 2018.
"In three of the past four years, Hollywood has had record box offices," he said. "We're actually expecting a reasonably robust box office in the U.S."
Disney's "Star Wars: Episode VII - The Force Awakens" became the highest grossing U.S. release after its December release, and 21st Century Fox's "Deadpool" smashed opening weekend records for the month of February.
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.
The transaction will be funded through a combination of existing liquidity and incremental debt. The debt financing commitment is being provided by Citigroup Global Markets.
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. The largest, Regal Entertainment Group, has 572 theaters and with 7,369 screens, according to its website.
Aron said he did not expect the deal to be derailed by a Justice Department investigation into whether an industry practice called film clearance is anticompetitive. AMC, along with Regal and Cinemark Holdings, last year received formal inquiries from the department related to an antitrust probe.
Film clearances are exclusive deals signed between large movie theater chains and film studios to limit the number of theaters allowed to screen certain movies, especially blockbusters. This keeps big movies out of smaller independent chains' reach, consumer activists say.
"AMC is happy in a clearance environment. We're happy in a nonclearance environment. If the Justice Department would like to rewrite the rules, we think we would prosper and thrive no matter how the rules change," Aron said.
Houston-based Viva Cinema sued AMC Entertainment last spring, saying AMC had coerced distributors to not license their films to it, which resulted in the theater's closure nearly seven months after its opening.
Chinese property and investment firm Dalian Wanda Group had acquired AMC Entertainment for $2.6 billion in 2012.
Dalian Wanda Group also agreed to acquire a majority stake in Legendary Entertainment earlier this year, valuing the U.S. movie studio company at $3 billion to $4 billion.
Chinese companies have been aggressively splurging on foreign acquisitions to sidestep slowing domestic growth. Chinese firms spent more than $100 billion on overseas acquisitions in 2015, the most ever.
In February ChemChina agreed to buy Swiss seeds and pesticides group Syngenta for $43 billion.
— Reuters contributed to this report.