According to the indictment by a New York federal grand jury, the two lied about the funds' prospects prior to collapse. One of the managers is also alleged to have carried out insider trading.
The indictment said that Cioffi transferred $2m of his $6m investment in one of the funds to another Bear Stearns fund with a higher return and failed to inform investors he had done so, despite being asked.
"Hedge fund managers remain subject to the same prohibitions against fraud as other market participants," Linda Chatman Thomsen, director of the Securities and Exchange Commission enforcement division, said.
When they choose to make public statements, they must not speak falsely or omit material information."
However, Susan Brune, Tannin's attorney, said that her client was being made a "scapegoat" for the market crisis and that "he looks forward to his acquittal".
Edward Little, Cioffi's attorney, in a statement said: "The subprime crisis took everyone by surprise, including the [US Federal Reserve] and Treasury, and dozens of the largest financial institutions have lost over $300bn to date on the same investments.
"Because [Cioffi's] funds were the first to lose might make him an easy target but doesn't mean he did anything wrong."
Wahid Farij, an expert on financial markets, told Al Jazeera the moves were significant as it showed there was accountability.
"What's critical when the economy is bad is the restoration of public trust, especially when Bear Stearns executives are charged with withholding information from the public."
Meanwhile, the Federal Bureau of Investigation also announced on Thursday that more than 400 people have been charged since March in a crackdown on mortgage fraud contributing to a US housing crisis.
"Operation Malicious Mortgage and the Bear Stearns case demonstrate that the Department of Justice is determined to detect and to punish mortgage fraud and to help restore stability and confidence in our housing and credit markets," Mark Filip, deputy attorney general, said.
The Operation Malicious Mortgage task force is investigating a variety of tactics including lending fraud, foreclosure rescue scams and mortgage-related bankruptcy schemes.