Hedge-fund manager Leon Cooperman and U.S. securities regulators ended their legal showdown Thursday with a $4.9 million settlement of insider trading allegations that does not bar the well-known investor from the industry.

The agreement with the Securities and Exchange Commission calls for Omega to accept a compliance monitor for five years who can question any trade that Mr. Cooperman or his traders make. It also calls for monthly certifications that insider information didn’t figure into any trades.

Neither Mr. Cooperman nor his firm Omega Advisors Inc. admitted to wrongdoing as part of the pact, according to a letter Mr. Cooperman sent to his investors. The SEC first accused Mr. Cooperman and Omega of insider trading in September 2016 following a five-year investigation.

Omega is one of the best known firms in the hedge fund industry, and the 74-year-old Mr. Cooperman is a prolific stock picker well-known for his appearances at conferences and on television.

“I am looking forward to putting this behind me now, instead of years from now,” Mr. Cooperman said in his letter to his investors. Mr. Cooperman declined additional comment when reached by phone.