Also on the docket are a final rule that would require mutual funds to provide their shareholders with simpler disclosures, and a proposal to limit investment advisers’ ability to outsource certain functions to third-party service providers.

The rule approved Wednesday was required by the 2010 Dodd-Frank Act to discourage fraud and accounting mischief. The so-called clawback rule’s implementation has been delayed for years amid resistance from Republican lawmakers and corporate executives.

SEC Chairman

Gary Gensler

reopened a 2015 proposal last year to collect fresh public feedback on the idea.

Mr. Gensler, a Democrat appointed by President Biden, said Wednesday that the rule will strengthen investor confidence in corporate reporting, as well as the accountability of managers.

“Corporate executives often are paid based on the performance of the companies they lead, with factors that may include revenue and business profits,” Mr. Gensler said. “If the company makes a material error in preparing the financial statements required under the securities laws, however, then an executive may receive compensation for reaching a milestone that in reality was never hit.”

The final version of the rule is broader than the 2015 proposal, which would have triggered clawbacks only if companies identified major accounting errors that required a restatement of prior years’ financial results. Under the approved rule, companies will also have to recover executive bonuses if they find smaller errors that affect only the latest year’s results.

SEC economists estimate the lesser category of accounting errors covered by the approved rule, known as “little r” restatements, are about three times as common as the more serious type.

Republican SEC Commissioner Mark Uyeda said the rule could lead companies to restructure compensation arrangements away from performance to shield executives from clawbacks.

“This may result in salary increases, rather than compensation mechanisms tied to financial-reporting measures,” Mr. Uyeda said, noting reports that companies are removing performance goals and replacing options with shares. He said the SEC’s approach “may ultimately weaken alignment of interests between shareholders and management.”

At least one study disputes that thesis.

A group of finance professors led by the University of Arizona’s Aazam Virani examined the stock-market reactions of S&P 1500 firms after the SEC unveiled the proposed clawback rule in 2015. They found that companies without existing clawback policies—those most likely to be affected by the rule—exhibited “positive abnormal stock returns” following the announcement.

The finding suggests that the adoption of a clawback policy “would, on average, enhance shareholder value for firms without an existing policy,” the authors wrote in a comment letter to the SEC in May.

GOP lawmakers and SEC commissioners and business groups, such as the U.S. Chamber of Commerce and Business Roundtable, had urged the agency not to move forward with the rule without doing more analysis. They criticized the decision to capture “little r” restatements in clawback policies and said the final rule’s definition of “executive officer” was overly broad.

Under the rule, firms will have to start including check boxes on the front page of their annual reports to highlight whether an error correction or clawback analysis has been conducted.

Companies will also have to adopt policies to recover wrongfully awarded incentive pay from both current and former executives, going back as many as three years. The rule will take effect in roughly one year.

Write to Paul Kiernan at paul.kiernan@wsj.com