First off, congrats! If you selected WA as primary residence when you applied in AADSAS, then chances are they have you listed as a WA resident. If not, you'll have a bit of work to do, but it's not too painful. You'll receive your offer packet in the mail in the coming weeks. One of the forms you'll receive is a residency confirmation form. It lists your address on it and asks you to confirm. If I remember correctly, this is the same form you send back with your deposit. This is basically all you can/need to do until you start hearing from the school next year.
Ultimately, you'll need to ensure you have a Washington driver's license or ID card, a Washington license plate (if you have a car), and a Washington address. You essentially have to turn over all loyalty to Washington State
. Because everyone's situation is always unique, you should contact the UW Residency Classification office with any specific questions pertaining to you. The website is:
https://registrar.washington.edu/students/residency/
You will also receive a call from the admissions office informing you of your acceptance. You can use that opportunity to ask about residency there too. Good luck!