The manager manager believes that the 55-year-old, who revealed he will step down in June, is making a "heartfelt" decision that could ultimately push the club forward
Gill has called time on his current at Old Trafford after 10 years in the position, and while he will remain as a director on the board, he will be concentrating on the 2013 Uefa Executive Committee elections as the Football Association's candidate.
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"I have been at United for over 26 years and for 23 of those years my boss has been one of only two men: Martin Edwards, who brought me to the club, and David Gill. I have enjoyed working with both," he told the club's official website.
"David has been a magnificent chief executive. Of course, we have had a million arguments, but I have always enjoyed them because I know that David has two great qualities: he is straight and he always puts Manchester United first.
"Him stepping down is a big loss to me but the fact that he is staying on the board encourages me that the reason for his departure is heartfelt, that he believes it is time for the club to move on."
Sir Alex regrets that he was unable to persuade Gill to stay in his role, but wishes him well for the future and believes he has always put the club first rather than himself.
"If I could have found a way of persuading him to stay I would love to have done that. But he has made his decision and I respect him for it," he added.
"He has been, and will continue to be, a fantastic success for Manchester United. He has all the qualities of successful people ingrained in him: energy, honesty, integrity, personality and decision-making ability. I wish him well in whatever new challenges he will tackle in the future.
"No disagreement is ever personal with him. He always wants the best for United, whether it's the players, the training ground or the staff."