Billionaire investor Carl Icahn on Wednesday was named special adviser to the president on overhauling federal regulations.

Mr. Icahn, who has spent the past four decades battling big companies as an activist investor, already has been wielding influence in President-elect Donald Trump’s transition team. He is playing a central role in selecting the next chairman of the Securities and Exchange Commission, people familiar with the matter said. Interested candidates have reached out to him, and he is interviewing others at the request of Mr. Trump, the people said.

The 80-year-old has played a similar role in identifying Mr. Trump’s choices for other important posts. Mr. Icahn, who controls an oil refiner and has spent months berating the Environmental Protection Agency over a rule he says hurts the industry, helped Mr. Trump vet candidates to run the EPA.

He weighed in enthusiastically as Mr. Trump considered whether to nominate Steven Mnuchin and Wilbur Ross to run the Treasury and Commerce departments, respectively. Both men were picked for the jobs.

The position isn’t an official government job; Mr. Icahn won’t get paid and won’t have to give up his current business dealings. Yet it is the latest example of a quintessential outsider assuming power as Mr. Trump assembles his cabinet secretaries and advisers

Messrs. Trump and Icahn say U.S. businesses have been overregulated in the Obama administration, which they argue is causing them to hold back on investments and is slowing the economy. Mr. Icahn will now be a key player in Mr. Trump’s efforts to loosen the regulatory reins.

“I’m involved with Donald where he wants me to be—I believe he respects my views and I think he listens to me,” Mr. Icahn said in an interview with The Wall Street Journal. “What Trump is trying to achieve is to show business in a lot of this country they aren’t going to be ruined by absurd regulation by bureaucrats.”

In a statement, Mr. Trump praised Mr. Icahn’s negotiating skills and said “his help on the strangling regulations that our country is faced with will be invaluable.”

Since the 1970s, Mr. Icahn has been an outspoken critic of many corporate boards, arguing the corporate-governance system is broken and impedes growth. He is a pioneer among activist shareholders, who buy up stakes and push boards to change direction by selling assets, firing the CEO or buying back shares.

An influential role shaping federal regulations marks a new chapter in Mr. Icahn’s influence on Wall Street. It would have been largely unimaginable in his early career as a brash outsider who picked fights with corporate titans. He was derided for years as a corporate raider. He was so feared by companies that they sometimes offered to pay him to go away, a 1980s tactic dubbed “greenmail” that was later restricted.

In recent years, Mr. Icahn’s views on shareholder activism have gone mainstream. These days, he generally manages to shake up corporate boards with less drama. He has taken stakes in giants such as Apple Inc., Xerox Corp., American International Group Inc. and eBay Inc.

As a prominent activist, Mr. Icahn has much at stake in the next SEC chairman. Activist fights are tightly controlled by the SEC. The agency issues rules that affect activists’ ability to do business and uses its enforcement arm to police their tactics. Activists and their corporate opponents regularly complain about the other side to the SEC.

The successor to current SEC Chairman Mary Jo White could have to decide whether activists will be forced to disclose their stakes more quickly after acquiring them and whether those disclosures need to include derivatives such as some stock options. Business groups that argue activists put their own short-term gains ahead of companies’ long-term futures urge such changes.

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Historically, Mr. Icahn had largely steered clear of Washington. But he was an early backer of Mr. Trump and advised him throughout the campaign. He urged Mr. Trump to support efforts to let U.S. corporations bring home offshore cash and to end the carried-interest tax break that benefits many on Wall Street.

Messrs. Trump and Icahn’s relationship dates back to their time running Atlantic City casinos. The pair sat together for the occasional big boxing match. Mr. Icahn’s wife, Gail, is on Mr. Trump’s inauguration committee.

Mr. Icahn is one of a handful of Wall Street powerbrokers who regularly get calls from the president-elect about their opinions on various topics.

Mr. Icahn, who calls himself a centrist, has said he wants to give back to the country. He often talks about how he rose from modest means to one of the nation’s wealthiest men. He has rejected criticism that he is only advising Mr. Trump to advance his own interests.

Billionaire activist-investor Carl Icahn speaks on the FOX Business Network in 2014. Photo: Reuters

The Democratic National Committee reacted quickly to the announcement, criticizing Mr. Icahn as conflicted given his investments and business dealings.

“It looks like Trump isn’t the only billionaire set to profit off of the presidency,” spokesman Eric Walker said in a statement.

Mr. Icahn has at times compared his helping Mr. Trump to turnaround companies with activism, where he benefits but also makes other shareholders billions. He has said other shareholders don’t complain about his own gains.

Shares of Mr. Icahn’s CVR Energy Inc., an oil refiner, have climbed 67% since the election, boosting the value of his investment by more than $600 million.

When Mr. Trump said early on in his campaign that he would consider Mr. Icahn as a potential Treasury secretary pick, Mr. Icahn declined the offer, joking he doesn’t get up early enough for the job.

Famed for late-night negotiations with CEOs, Mr. Icahn has ribbed Mr. Trump about his own nocturnal habits. “I told him when you’re done tweeting, call me,” Mr. Icahn said. “I’ll be up.”

Write to David Benoit at david.benoit@wsj.com