Provided herein are processes for topically applying an antimicrobial finish to a textile substrate, such as a yarn, a fabric, a composite, or an assembled article (for example, a garment). Specifically, the antimicrobial finish is based on hindered amine compounds that are applied in an aqueous bath (such as a commercial or home laundry setting), using the factors of pH and compound solubility to promote the formation of a durable antimicrobial halamine finish. Advantageously, the antimicrobial finish, which may be applied to fabrics made of any of a variety of fiber types and combinations of fiber types, has been found to be durable to repeated launderings.