Cellino's company Eleonora Sport Limited completed its protracted purchase of 75% of the Elland Road club's shares following a successful appeal against the Football League's decision to block the takeover.
The League, who have still to ratify the takeover, ruled that the Italian's recent conviction of tax evasion in a Sardinia court - one he is appealing - disqualified him under its owners and directors test.
In January, a lawyer, believed to be acting on Cellino's instruction, sacked McDermott before he was then reinstated a day later.
It has been reported that Cellino would now officially sack McDermott following a run of eight defeats in nine games.
However, the 57-year-old, who spoke with McDermott before the 3-0 loss at Watford on Tuesday, says the former Reading boss will remain at Leeds until the end of the season.
When asked by Sky Sports if McDermott would stay, Cellino said: "I hope so. 100%. He is a good guy."
Prior to his takeover, Cellino was embroiled in a row with then owners GFH Capital over who was responsible for funding the club, which resulted in McDermott's backroom staff and playing squad agreeing to defer half their wages for March.
Another chunk was paid to the staff and players last week and Cellino says his first job is to take care of the wages and tax before thoughts turn to matters on the pitch.
"I have to pay the wages and the tax, then we have to address things for the next season," he added.
"This one is already finished so we need to have a couple of good games between now and then."
Leeds are currently 16th in the Championship with 47 points, six places and eight points above the relegation zone with five matches still to play.