My husband is in the process of doing the same thing, his two girls are living with us and both him and Mom have agreed to switch physical custody to him. What they are doing is typing up a stipulation that transfers physical custody to him and outlines when child support should stop (from him to her), who will be covering the children's medical insurance, who is responsible for uninsured medical costs, visitation schedules, and issues of who can claim the children on taxes. My husband is not asking for child support from her. They will both sign the document in front of a notary and submit it to the court along with a typed up custody order for the judge to sign off on. From what we've been told by several lawyers here in Minnesota, as long as BOTH parents are agreeing to switch custody, it's pretty much a done deal. My husband and his ex never went through a custody battle in the divorce, but resolved everything through mediation. We are doing everything pro-se, but with the guidance of the Father's Resource Center here and the lawyers that volunteer there.
You may have to go ahead and file a motion to stop child support separately with CSE. If you can show that you are being given physical custody that should be enough for them. Keep in mind that if you owe arrearages, unless she agrees to waive them, you will still owe them regardless. This is also true if she collected public assistance and your arrearages are a result of paying back welfare.
You will have to check the laws in your state and perhaps at least obtain a free consultation with a lawyer to get some advice on what the process is in your particular state. Many times courts will offer pro-se packages of paperwork also.
Good luck!