New York — In a move that formalizes a long-anticipated succession, Donald Trump Jr. and Eric Trump announced Thursday that they will assume full operational control of the Trump Organization, the sprawling real estate and branding empire built by their father, Donald J. Trump.

The announcement, made at the company’s Fifth Avenue headquarters, confirmed that the elder Mr. Trump will retire from public life and step away from day-to-day business activities after more than four decades in the spotlight. “Our father has accomplished everything he set out to do in business,” Donald Jr. said in a prepared statement. “Eric and I are honored to continue his legacy and maintain the standards of excellence he established.”

Eric Trump added that the company’s leadership transition would be “seamless,” with no major changes to management structure or business priorities. “The same team that has guided the Trump Organization’s success will continue to operate as before,” he said.

The announcement comes after months of speculation about Mr. Trump’s future role in the company. People close to the family described the decision as the culmination of a gradual handoff that began several years ago, as the younger Trumps took increasing responsibility for new developments and global licensing deals.

Under their direction, the company has expanded its hotel and golf operations overseas, with projects in Dubai, Scotland, and the Philippines. Analysts say the brothers’ management style differs in tone from their father’s but not in ambition.

“Don Jr. and Eric are pragmatic operators,” said Melissa Tanner, a hospitality industry analyst with Greenleaf Partners. “They’re maintaining the Trump brand’s focus on luxury and visibility while avoiding unnecessary risk.”

A company spokesman said Ivanka Trump, the eldest daughter, will continue to serve as executive vice president, overseeing design and development initiatives across several hotel and residential projects.

In a brief statement released through the Trump Organization, the elder Mr. Trump thanked his employees, partners, and “the incredible people who have made our company the best in the world,” adding that he plans to “enjoy life and reflect on all we’ve built together.”

While the transition marks the end of an era for one of New York’s most recognizable figures, those familiar with the company say little will change in its day-to-day operations.

“The Trump name is a brand unto itself,” said David Ressler, a professor of marketing at Columbia Business School. “The question now is how that brand evolves without the personality who defined it.”