Cellino, 57, was recently found guilty of tax evasion by a court in Italy.
The businessman was ordered to pay a fine of €600,000 (£502,000) for failing to pay import duty on his yacht.
Cellino, who owns Serie A side Cagliari, agreed to purchase a 75% stake in Leeds last month but has now seen the deal fall through following the Football League's ruling.
"At its meeting yesterday evening, the Board of The Football League considered the eligibility of Massimo Cellino under its Owners' and Directors' Test," read an official statement.
"The Board considered detailed legal advice with regard to the application of its regulations within the context of a decision made under Italian law.
"Mr. Cellino was recently found guilty beyond reasonable doubt by a Court in Sardinia of an offence under Italian tax legislation relating to the non-payment of import duties on a boat. This resulted in a fine of €600,000, an order for the payment of trial costs and the confiscation of the boat in question.
"Having fully considered the matter, the Board agreed unanimously that the decision of the Italian Court does constitute a disqualifying condition under its Owners' and Directors' Test.
"The relevant disqualifying condition being that Massimo Cellino has been convicted of an offence involving acts that would reasonably be considered to be dishonest.
"In line with Football League regulations, Massimo Cellino is entitled to appeal against the Board's decision within 14 days. In such circumstances, The League would seek to expedite the process to deliver certainty to all parties in the shortest possible timeframe."
Cellino has been supporting Leeds financially for the past two months but announced on March 12 that he would wait for the Football League's decision before choosing whether to continue his investment in the club.