In MGM, Amazon will get a library of more than 4,000 films, including franchises such as James Bond and Rocky, and classics such as “The Silence of the Lambs,” “Raging Bull” and “12 Angry Men.” The TV catalog includes critically acclaimed shows such as “The Handmaid’s Tale,” “Fargo” and “Vikings.”

“The acquisition’s thesis here is really very simple,” Amazon Chief Executive Officer

Jeff Bezos

said on a call with shareholders later Wednesday. “MGM has a vast, deep catalog of much-beloved intellectual property, and with the talented people at MGM and the talented people at Amazon Studios, we can reimagine and develop that IP for the 21st century.”

Amazon said in February that Mr. Bezos would be stepping down as CEO in a leadership change that leaves top lieutenant Andy Jassy to oversee MGM’s integration into the company when he takes the reins as CEO on July 5.

MGM Chairman Kevin Ulrich had sought $10 billion for the company, scaring off some potential suitors, such as

Apple Inc.

and

Sony Group Corp.’s

Sony Pictures Entertainment, a person close to him said. Amazon, hungry for more content for Prime Video, had a greater appetite than others.

The tech company had approached MGM multiple times over the past 18 months, according to people familiar with the talks. At one point in their discussions, MGM and Amazon executives weighed a possible deal to bring the latest James Bond film to the Amazon’s streaming service while movie theaters remained closed during the pandemic, according to a person familiar with the matter.

Late last year, Mike Hopkins, senior vice president of Prime Video and Amazon Studios, contacted Mr. Ulrich and subsequently took the lead on merger talks, which for months didn’t move past the exploratory stage, according to people familiar with the matter. That changed about five weeks ago, when the tech company made its more than $8 billion offer.

The board quickly signed off, and the two reached an agreement Monday, according to people close to the deal. The companies decided to hold the announcement for Wednesday out of sensitivity that Tuesday was the first anniversary of George Floyd’s murder by a police officer in Minneapolis, the people said.

Besides MGM, Amazon also approached Sony Pictures Entertainment about an acquisition but was rebuffed, a person familiar with the matter said.

Amazon is facing antitrust scrutiny from U.S. and foreign regulators over a range of its business practices. Sen. Amy Klobuchar (D., Minn.) said Wednesday that the MGM deal should be subject to a federal probe.

“This is a major acquisition that has the potential to impact millions of consumers,” she said in a statement. “The Department of Justice must conduct a thorough investigation to ensure that this deal won’t risk harming competition.”

The acquisition is the latest in a series of mergers that are shaking the entertainment industry as media and tech companies fight for supremacy in the streaming age.

Earlier this month,

AT&T Inc.

said it would spin off its WarnerMedia assets and merge them with

Discovery Inc.

In recent years, Disney bought most of the entertainment assets of 21st Century Fox, and

Viacom Inc.

recombined with CBS Corp., all part of efforts to amass content and build direct-to-consumer streaming services.

Media executives have buzzed for years about the possibility of mergers with companies such as Amazon and Apple, but the tech companies avoided big-ticket deals as they built out their streaming platforms.

Now the landscape is shifting. Traditional studios are keeping more content for their homegrown streaming services, such as NBCUniversal’s Peacock and WarnerMedia’s HBO Max, instead of licensing it to the likes of Amazon and Netflix. Owning MGM would help Amazon better control its destiny in the streaming wars.

The James Bond franchise is among the most important content Amazon is taking hold of and comes with added complexity. The producers Barbara Broccoli and Michael Wilson essentially control the property’s creative and business operations.

Mr. Hopkins called the producers before the deal closed to reassure them that the franchise would be in good hands at Amazon, people familiar with the call said. In addition, Ms. Broccoli has a long friendship with Jen Salke, who heads Amazon’s TV and movie operations.

Amazon agreed that all James Bond movies currently in the pipeline would continue to have a theatrical release. “Barbara and Michael still have control and are protected,” one of the people close to the deal said.

Although Amazon has deeper pockets than any other players in the streaming business, its Prime Video service hasn’t had the massive creative successes that Netflix and newcomer Disney+ have enjoyed. It made several critically acclaimed movies and TV shows including “Transparent,” “Manchester by the Sea” and, more recently, “One Night in Miami.”

Entertainment isn’t the only content on which Amazon is spending heavily. In March it struck a deal with the National Football League for exclusive rights to Thursday Night Football at a price of $1.2 billion a season over 11 years, people with knowledge of that transaction said.

—Cara Lombardo, Benjamin Mullin and Erich Schwartzel contributed to this article.

Write to Joe Flint at joe.flint@wsj.com