A brush seal for use between a rotating component and a stationary component in a turbomachine is disclosed. The brush seal according to embodiments of this invention includes a set of bristles having a fixed end and a free end, wherein the fixed end is attached to the rotating component with a mechanical clamping element and the free end extends towards the stationary component, and wherein the set of bristles are angled axially at an axial angle with respect to the rotating component. In one embodiment, the fixed end of the set of bristles are wrapped at least partially around a core element and the clamping element partially surrounds the core element and the fixed end of the set of bristles, wherein the clamping element secures the fixed end of the set of bristles within a circumferential groove in the rotating component.