The 57-year-old has been involved in a protracted saga to buy a majority stake in the Championship club.
The Football League banned Cellino from taking over Leeds last month after he was convicted of tax evasion.
However, the businessman successfully appealed against their decision on April 5, allowing him to carry on with his buyout of the club.
Cellino's company Eleonora Sport has now bought 75% of the shares at Elland Road, with Cellino taking a place on the board of directors.
"Massimo Cellino has now been appointed a director of LUFC Holdings & ESL has completed its purchase of 75% of the shares of LUFC Holdings," Cellino's legal representatives Mishcon de Reya tweeted.
Leeds are yet to confirm whether Cellino has completed his takeover.