The 71-year-old will step down as manager at the end of the season to take up a role as a director, while Everton boss David Moyes is set to succeed the Scot at Old Trafford
Meanwhile, Gill has revealed that the club have already begun planning for Sir Alex's retirement but insists that the United boss will be involved with making the next managerial appointment.
"It is a new era and I look forward to watching a successful Manchester United team on the pitch," the chief executive, who will also leave his post in the summer, told MUTV.
"It is a momentous day for the club, the fans and the whole football world. Working with Sir Alex has been the highlight of my career.
"We knew this day would come and we have been preparing for this," Gill continued. "The board will take council from Sir Alex and Sir Bobby [Charlton] on the new appointment.
"Everyone can rest assured the new manager will get the necessary space and necessary opportunity to do his job without interference.
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"The qualities [needed] are the ones that have been inherent in Manchester United for many years. If you look at what has happened with the two most successful eras – Sir Matt Busby and Alex – they are managers who got involved in the whole aspect of the club, whether it be from the youth team up to the first team.
"All aspects of it, plus that degree of loyalty and the understanding of the football club that it's not just what happens on the first-team pitch, is crucial to the success of Manchester United. Those are the sort of things we’ll be looking at.
"Clearly he has to have the requisite football experience, both in terms of domestic and European experience, so I think it's a small pool but we'll move forward."