Two longtime executives of the entertainment empire that AT&T Inc. T 0.12% bought for more than $80 billion are stepping down, as the telecommunications giant gets ready to put its stamp on WarnerMedia days after the last antitrust hurdle to the deal was cleared.

Richard Plepler, the chairman and chief executive of HBO, said he was resigning in a memo to staff Thursday afternoon. David Levy, president of Turner, the parent of cable channels CNN, TNT, TBS and Cartoon Network, is also stepping down—perhaps as early as Friday, people familiar with the matter said.

“Hard as it is to think about leaving the company I love, and the people I love in it, it is the right time for me to do so,” Mr. Plepler wrote in his memo.

The resignation of Mr. Plepler, who has led HBO since 2013 and played a prominent role in many successful shows including “Game of Thrones” and “Veep,” comes as AT&T overhauls the operations of Warner Bros., HBO and Turner. Under previous owner Time Warner and its then-chief executive Jeff Bewkes, these units had operated very autonomously.

John Stankey, the executive AT&T put in charge as chief executive of WarnerMedia, said Thursday that Mr. Plepler’s “vision, energy and passion helped to elevate HBO’s brand to what it has become today.”

AT&T is in advanced talks with veteran television executive and producer Robert Greenblatt to take a senior role at WarnerMedia—as Time Warner was rebranded—that could include oversight of a new unit that would combine HBO and Turner entertainment networks and a coming streaming service, The Wall Street Journal reported Wednesday.

The shake-up is a gamble for AT&T, which has seen its bottom line benefit over the past six months from hit shows and movies developed by Time Warner executives. In an interview last year with the Journal, Chief Executive Randall Stephenson said AT&T would treat WarnerMedia differently than past acquisition targets because of the “creative imagination” needed for a media business to succeed.

“You need to guard that culture with your life,” Mr. Stephenson said at the time. “By that same token, the business model does have to change.”

HBO faces intensifying competition from streaming-media rivals, especially Netflix Inc., which is spending huge sums on content and whose subscriber base is growing at a fast rate.

Ever since the AT&T deal, there was speculation about how the urbane Mr. Plepler would fit in with his new telephone-company bosses. While both were on the same page about the need to invest more in programming for HBO, Mr. Plepler chafed at the increased oversight from his new overlords, people close to him said.

Mr. Plepler wanted to focus his priorities on continuing to have quality award-winning fare on HBO while his new bosses are concerned with determining the best way to exploit all its content on AT&T’s various platforms. At times, those two visions clashed, people close to the situation said.

As much as Mr. Plepler pined for more money for programming, he was wary of trying to turn HBO into a new version of Netflix, which launches new shows seemingly every day, many of which disappear into the abyss of the streaming service.

“More is not better. Only better is better,” Mr. Plepler told the Journal in a 2017 interview describing the channel’s strategy.

Mr. Plepler’s resignation was regarded as a seismic event within HBO, which is undergoing a round of voluntary buyouts as part of the merger, according to people familiar with the matter.

A bon vivant known for his charm, style and perennial tan, Mr. Plepler was seen as one of the more magnetic and compelling executives in the ranks of the entertainment industry. The night before he resigned, he and several other top HBO executives had dinner with Oprah Winfrey.

Earlier this week, AT&T finally emerged victorious in its battle against the Justice Department, which attempted to thwart the deal but was defeated in court for the second time.

It is unlikely that either Mr. Plepler or Mr. Levy will be replaced, a person familiar with the matter said.

Within Turner, Mr. Levy is known as a consummate deal maker, a charismatic presence who cultivates the unit’s lucrative relationships with the National Basketball Association and the National Collegiate Athletic Association.

An affable and gregarious figure, Mr. Levy has been seen as an approachable and down-to-earth executive. He loves a good laugh and even had sportscaster Marv Albert record the voice-mail message on his cellphone.

Some within Turner are cautiously optimistic that Mr. Levy’s exit will give AT&T a freer hand to remake what they regard as a staid corporate culture that hasn’t kept pace with the rise of streaming and digital media, people familiar with the matter said.

If AT&T is able to negotiate a deal with Mr. Greenblatt, he would likely serve as chief content executive for both HBO and Turner. Mr. Greenblatt was most recently president of Comcast Corp.’s NBC network and its sister studio Universal Television. Before that he was president of CBS Corp.’s premium cable channel Showtime.

Mr. Greenblatt would also have a hands-on role in WarnerMedia’s new direct-to-consumer streaming service, which it aims to launch later this year. Kevin Reilly, the head of entertainment for the Turner networks, is directly responsible for programming strategy in the streaming service and will stay in that role, a person familiar with the matter said.

A former head of communications for HBO, Mr. Plepler rose through the ranks to programming executive and then CEO. During that time, HBO grew into a cash cow for parent Time Warner as its movie studios and commercial cable networks faced challenges from streaming services and cord-cutting. At the same time, the emergence of Netflix and Amazon forced HBO to up its game in terms of spending for content. It also launched its own direct-to-consumer service—HBO Now—in response to the rising popularity of digital platforms.

Mr. Plepler had been sending signals for the past few months that he was reconsidering his role at HBO, people close to him said. It had become clear that the freedom Mr. Plepler had enjoyed before the then-CEO Mr. Bewkes sold Time Warner to AT&T was a thing of the past.

“Thanks Jeff Bewkes,” one HBO executive said sarcastically Thursday.

—Drew FitzGerald contributed to this article.

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