Billionaire investor Steven A. Cohen reached a settlement with regulators that clears him to return to managing out side money in two years, a remarkable turnaround for the Wall Street veteran after years of legal fights.

Long a target of law-enforcement authorities, Mr. Cohen’s SAC Capital Advisors LP pleaded guilty to insider trading in 2013, paid $1.8 billion in penalties, and shrank to manage only his own fortune. One of his confidants at SAC was convicted, and the Securities and Exchange Commission sought to have Mr. Cohen barred for life from the industry. Mr. Cohen was never criminally charged.

But a 2014 appeals court ruling overturning insider-trading convictions in a related case weakened the case against Mr. Cohen, paving the way for Friday’s settlement.

The pact with the SEC restricts Mr. Cohen for two more years from serving as a supervisor at a registered fund before allowing him to get back into the business that made him one of the country’s most-profitable hedge-fund managers. During that time, his firm will be subject to SEC exams. It will also require the firm to hire an independent consultant to review the firm’s compliance procedures and implement any recommended fixes.

The settlement also extends oversight if the SEC takes any new actions against Mr. Cohen. The provisions essentially allow the SEC to keep close watch on a firm that it wouldn’t otherwise have a window into.