Cellino, who is also chairman at Serie A outfit Cagliari, failed the Football League's 'fit and proper person' test for owners and directors after agreeing to buy a 75 per cent stake in the Yorkshire club in February.
But Cellino was successful with a subsequent appeal, paving the way for the deal to be completed.
In a statement, a Football League spokesman said: "At its meeting in London today, the board of directors of The Football League considered the outcome of the recent appeal by Massimo Cellino under the owners' and directors' Test.
"In making its original decision, the board took the view that Mr Cellino's recent conviction (for tax evasion) in Sardinia was for an act that 'would reasonably be considered to be dishonest' and that he was therefore subject to a disqualifying condition.
"In the current absence of detailed reasons for the conviction from the Sardinian Court and having taken into account the principles of Italian law, an independent QC reached a different conclusion. On this basis, Massimo Cellino is cleared to be a director of Leeds United."
Cellino was in attendance to watch Leeds crash to a 3-0 defeat at Watford on Tuesday - the club's eighth loss in their last nine matches.
Leeds have plummeted to 16th in the table, with the future of manager Brian McDermott the subject of much speculation.
But Cellino has confirmed that the former Reading boss will stay at the helm at least until the end of the season.
He told Sky Sports: "For the moment the important thing at Leeds is to pay wages and bills.
"Then we will start thinking about next season, given that although there are still some matches left the current season is practically over.
"I will meet with McDermott as soon as possible in order to discuss the future. He seems like a good person and he will remain here."
Cellino has targeted a Premier League return for Leeds - three-time champions of England - by 2016.
