Mr Williams used a video announcement to accuse the British billionaire of using inside information to "shower gifts on his friends and lovers".
Mr Lewis "has been indicted and will face justice" in the Southern District of New York (SDNY), Mr Williams said.
BBC News has approached Tottenham Hotspur and Mr Lewis for comment.
In the video statement, posted on Twitter, Mr Williams set out a series of allegations against Mr Lewis. A formal written statement, known as an indictment, has yet to be released.
"We allege that, for years, Joe Lewis abused his access to corporate board rooms and repeatedly provided inside information to his romantic partners, his personal assistants, his private pilots, and his friends," Mr Williams said in the video.
Mr Williams, the chief federal law enforcement officer for the SDNY, alleged that Mr Lewis's acquaintances used that information to make millions of dollars in the stock market.
"Thanks to [Mr] Lewis, those bets were a sure thing," he claimed.
Mr Lewis owns hundreds of assets, including Premier League London club Spurs and a stake in UK pub chain Mitchells & Butlers. Forbes magazine has recently estimated his fortune at £4.73bn ($6.1bn).
-- Courtesy of BBC Sport