Advertising giant WPP PLC will pay $19 million to resolve government allegations that it failed to adequately guard against corruption risks in India, China, Brazil and Peru, securities regulators announced Friday.

The Securities and Exchange Commission said the compliance gaps surfaced as WPP implemented an aggressive growth strategy that involved buying smaller advertising firms in high-risk markets. The acquired firms’ founders would often stay on as chief executive and have broad autonomy, the agency said.

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Advertising giant WPP PLC will pay $19 million to resolve government allegations that it failed to adequately guard against corruption risks in India, China, Brazil and Peru, securities regulators announced Friday.

The Securities and Exchange Commission said the compliance gaps surfaced as WPP implemented an aggressive growth strategy that involved buying smaller advertising firms in high-risk markets. The acquired firms’ founders would often stay on as chief executive and have broad autonomy, the agency said.

Like other big ad conglomerates, WPP—the world’s biggest by revenue—grew largely through buying up agencies around the world. In many cases those deals involved provisions that afforded top executives bonuses for meeting certain financial goals. Those types of deals could motivate executives at the acquired firms to increase their profits any way they could, said Doug Wood, senior counsel at law firm Reed Smith LLP and general counsel to the Association of National Advertisers.

The SEC said an Indian subsidiary of WPP paid as much as $1 million in bribes to Indian officials through intermediaries to obtain and retain government business, resulting in about $5.7 million in additional profits between 2015 and 2017. The bribes continued even though WPP had received seven anonymous complaints over that period referring to the conduct, the agency said.

In China, a subsidiary in the midst of a tax audit avoided paying more than $3 million in taxes to a Chinese tax authority by giving $2,000 worth of gifts and entertainment to tax officials and making more than $100,000 in payments to a vendor recommended by tax officials ahead of the audit’s completion, the SEC said. An employee of the WPP China subsidiary falsified documentation to justify the vendor payments, regulators said.

The SEC also found that a WPP subsidiary in Brazil made improper payments to vendors in connection to securing government contracts, while a WPP subsidiary in Peru agreed to be a conduit for a construction company’s bribes to the mayor of Lima’s political campaign.

The SEC said the alleged wrongdoing violated the Foreign Corrupt Practices Act, a law that bars U.S.-listed companies from paying money or anything of value to overseas officials in order to win business. WPP agreed to settle the SEC’s probe without admitting or denying the claims.

WPP said it had terminated employees accused of wrongdoing and cooperated with the SEC’s investigation. “WPP’s new leadership has put in place robust new compliance measures and controls,” the company said in a statement. WPP also said it “fundamentally changed its approach to acquisitions.”

The fine includes $10 million in profits that WPP must pay back, $1 million in interest on that amount and an $8 million penalty.

“A company cannot allow a focus on profitability or market share to come at the expense of appropriate controls,” said Charles Cain, chief of the agency’s FCPA enforcement unit. “Further, it is essential for companies to identify the root cause of problems when red flags emerge to prevent a pattern of corrupt behavior from taking hold.”

The bulk of the issues found by the SEC took place while WPP founder Martin Sorrell was at the helm. From 1986 to 2018, Mr. Sorrell transformed a little-known manufacturer of wire shopping carts into a global advertising powerhouse, home of a raft of blue-chip creative agencies like J. Walter Thompson and Young & Rubicam as well as powerhouse media-buyer GroupM.

“My personal commitment to compliance and controls during almost fifty years of value creation has been rigorous and remains so,” Mr. Sorrell said in a statement. He said he had no involvement in the settlement between the SEC and WPP.

WPP operates in over 100 countries. WPP’s current chief executive officer, Mark Read, has been streamlining the company’s operations including merging several major agencies, disposing of 60 noncore businesses and investments, and closing 80 business units in 2020, according to the company’s annual report.

WPP currently owns or has majority ownership in 2,241 companies, which is down from 2,829 in April 2017, the company said.

Mr. Read was first briefed on the SEC investigation after becoming co-chief operating officer in 2018, according to a person familiar with the matter. By then, the agency had already been investigating the matter for years, the person added.

The SEC’s action against WPP illustrates an issue holding companies can have with respect to the manner in which they acquired local agencies over the years, said Mr. Wood, the ANA general counsel.

It can be difficult for holding companies to “adequately manage hundreds of subsidiaries, many of which were in countries with little or no regulatory oversight,” Mr. Wood said.

Write to Dave Michaels at dave.michaels@wsj.com and Suzanne Vranica at suzanne.vranica@wsj.com