Cellino was due to begin an 18-month suspension on February 1 after the FA found him guilty of breaking its agency regulations in relation to the 2014 sale of Ross McCormack to Fulham.
The Italian immediately declared his intention to appeal against the verdict, which was handed out on December 8.
The club and Cellino were each fined Â£250,000 as part of the ruling.
Leeds said in a statement: "As stated in his message to supporters following the initial decision, Mr Cellino has lodged an appeal to overturn the guilty verdict and any sanctions imposed upon Mr Cellino by the FA will be held/suspended until the appeal has been heard and a verdict has been found.
"We can also confirm that the club has lodged an appeal in relation to the sanctions that were imposed directly on us
We are confident that the appeals will be successful.
"Everybody at the club is completely focused on supporting Garry Monk and his team for the rest of this season
The club will make no further comment on Mr Cellino's appeal until the process is complete."
Earlier this month Cellino sold half of his stake in Leeds to fellow Italian Andrea Radrizzani
Leeds currently sit third in the Sky Bet Championship.
Source : PA