In The Shawshank Redemption, Andy spent years carving a tunnel from his cell to the sewers which was hidden behind posters of various pin-ups.
This question: How was Andy Dufresne able to dig the tunnel for many years without being discovered? - covers why no one ever looked behind the poster.
However, if he was ever transferred to another cell or another prison, his ruse would be instantly discovered. How did he know this wouldn't happen? Or was he just willing to take the risk?
The warden’s arrangement becomes clear when Andy tells him he has someone who can help exonerate him for his crime. When the warden refuses to help and throws Andy in solitary, Andy states that he will stop laundering the warden’s money. The warden responds that Andy will do what he is told or he will lose his privileges:
Nothing stops. Nothing, or you will do the hardest time there is. No more protection from the guards. I’ll pull you out of that one-bunk Hilton and cast you down with the Sodomites.
The implication of these lines is that Andy was getting the private cell and the protection because he was useful to the warden. As long as Andy played ball, he was unlikely to be moved.
Andy was doing warden a very big favor by covering his black money tracks. He might have made a deal with warden to keep him in the same cell.
