Mr. Trump has also promised to edit the federal rule book, removing what he has described as overly burdensome restrictions. He said last month that the government would eliminate two regulations for each new rule it put on the books. For Mr. Icahn, who will not draw a salary, the new role formalizes his relationship with Mr. Trump, whom he advised on economic issues throughout the campaign. Mr. Icahn, 80, has no experience in government; like a growing number of Mr. Trump’s appointees, he was prized for his success as a businessman.

Mr. Icahn, a brash New York billionaire who vocally supported Mr. Trump during the campaign, made his fortune as a “corporate raider,” buying stakes in corporations and demanding changes to reward shareholders. “Carl was with me from the beginning, and with his being one of the world’s great businessmen, that was something I truly appreciated,” Mr. Trump said in a statement. “His help on the strangling regulations that our country is faced with will be invaluable.”

Mr. Icahn will also play a role in the selection of a new chairman for the Securities and Exchange Commission, the regulator that serves as the referee for his battles with corporations.

Mr. Icahn, the child of two New York schoolteachers, was not known for political activism before the 2016 campaign, and he has insisted that he wants to help the country, not himself. But Mr. Trump’s choice of a major corporate investor to play a role in rewriting regulations that could affect those companies renewed concerns about conflicts of interest in the next administration.