Leeds supporters groups have expressed their concern over the takeover as the 57-year-old businessman has a criminal conviction for fraud in his homeland.
"I am delighted to announce we have exchanged contracts for the sale of 75 percent of the club to Eleonora Sport Limited subject to Football League approval," Leeds chairman Salah Nooruddin said in a statement.
Nooruddin added that parent company GFH Capital and its investors would retain a 25 percent stake in the club and that he was remaining as chairman.
"The board has always had as its principal aim ... to build on the foundations we have laid for sustainable success for this great club," he said.
"We believe we have achieved that with this deal. It provides the basis from which Leeds United can move forward to a position which will enable it once again to compete at the highest levels of football.
"That is where this great club belongs and it is nothing less than its fans deserve. Throughout the difficult years, as well as the glory years, they have remained second to none in their support of the club and we as a board have always appreciated their passion," said Nooruddin.
The Cellino family have been involved with Serie A team Cagliari since 1992 and plan to invest "substantially" in their new English club.
Leeds, top-flight champions in 1969, 1974 and 1992, were relegated from the Premier League in 2004 and are 11th in the Championship going into Saturday's game at rock bottom Yeovil Town.
The Yorkshire club were also European Cup runners-up in 1975 and reached the semi-finals of the Champions League in 2001.
The takeover could put the position of manager Brian McDermott in doubt.
McDermott was briefly sacked by Cellino last week, according to media reports, before being hastily re-instated by the existing board.
(Editing by Tony Jimenez)
