A former Massachusetts Institute of Technology professor and his son agreed to plead guilty to charges stemming from a scheme to lure investors to their hedge fund with false promises about investment strategies, according to federal prosecutors.

Gabriel Bitran, a former professor and associate dean of MIT’s Sloan School of Management, and his son, Marco Bitran, lied to investors in GMB Capital Management LLC who provided more than $500 million to the fund, prosecutors in Boston said. The Bitrans’ funds incurred losses of more than $140 million of investors’ money while they paid themselves millions of dollars in management fees, prosecutors said.

In 2009, while investigating potential victims of Bernard L. Madoff’s fraud, U.S. regulators began probing Bitran’s claims that their funds had average annual returns of 16 percent to 23 percent, according to prosecutors.

In April 2012, the Bitrans agreed to pay $4.8 million to settle the U.S. Securities and Exchange Commission claims that they lured customers with a fabricated track record before investing with other funds, including Madoff’s.