You need to file to modify custody. If you both agree, it can be done quickly and simply.
I would encourage you to hire an attorney to draft the paperwork. You could try to do it yourself but I assume that time is of the essence since you don't want her to change her mind.
This is the best website that I'm aware of to find an attorney to help you.
Find a lawyer in your county to do it for you.
If you need help, let me know at 713-847-6000. If you call me over the week-end, I'll try to pick up the phone or leave a message & I'll call you back. My direct email is email@example.com
Fran Brochstein has over 20 years legal experience & enjoys educating the public about Texas laws. She is a full-time family law mediator in the Houston area. If you found this answer "helpful" or "best answer", please select the button to show your appreciation. Please understand that this is not a personal consultation and in no way creates an attorney-client relationship. You are strongly encouraged to consult with an attorney in your county in person about your specific legal problem. You can contact her at 713-805-9591 - 7 days a week - her personal cell phone.
You would need to file a modification, then do a judgment and a waiver. Most court requires an appearance by the moving party if changing custody, so you will have to go to court once to prove up the deal.