Hearn has been chairman of the London outfit since 1995, when he acquired a controlling stake from Tony Wood.
A statement on the club's official website on Monday confirmed the news, with Becchetti now set to take over as chairman.
"Barry Hearn has completed the sale of his stake in Leyton Orient Football Club to Francesco Becchetti," the statement read.
"Hearn's company Matchroom Sport Ltd's 90 per cent shareholding in the club has passed to the Italian businessman, who will become the club's new chairman.
"Hearn, his son Eddie, Steve Dawson and David Dodd have resigned from the board of directors whilst Matthew Porter has stood down as chief executive but will remain as a director of the club."
Under the guidance of Russell Slade, Orient reached the League One play-off final at the end of the 2013-14 campaign, only to suffer heartbreak at Wembley.
Leading Rotherham United 2-0 at half-time, Orient were pegged back to 2-2 by the final whistle and went on to lose 4-3 on penalties.
