It depends. Usually, It need take weeks to months and sometimes, it may need longer time. Anyway, i think you can ask your ophthalmologist how long will it takes for cure uveitis. The ophthalmologist who diagnose your eyes will know better than about your eyes than others. So, you needn't ask options from internet, your ophthalmologist is the best resources and guide to help you cure uveitis.
It may take weeks to months for uveitis to heal. If it is serious enough, it may take even longer time to get healed. Once you find you have got uveitis, you'd better have it treated as early as possible. Otherwise it will cause serious problems if it is untreated for a long time. Talk to your doctor about your problem to seek for proper treatment for your uveitis. I hope you can have your uveitis treated soon. Good luck!