The 71-year-old Scot announced on Wednesday morning that he will stand down at the end of the season after a trophy-laden 26-year reign, having celebrated his 49th and final piece of silverware with a 13th Premier League title this term.
Gill said: "I've had the tremendous pleasure of working very closely with Alex for 16 unforgettable years - through the treble, the double, countless trophy wins and numerous signings.
"We knew that his retirement would come one day and we both have been planning for it by ensuring the quality of the squad and club structures are in first-class condition.
"Alex's vision, energy and ability have built teams - both on and off the pitch - that his successor can count on as among the best and most loyal in world sport.
"The way he cares for this club, his staff and for the football family in general is something that I admire. It is a side to him that is often hidden from public view but it is something that I have been privileged to witness in the last 16 years.
"What he has done for this club and for the game in general will never be forgotten. It has been the greatest experience of my working life being alongside Alex and a great honour to be able to call him a friend."