A prosthetic heart valve for replacing a native valve includes a collapsible and expandable stent having a proximal end and a distal end, and a valve assembly including a plurality of leaflets, the valve assembly being disposed within the stent. The heart valve further includes a first plurality of elongated legs coupled to the stent and transitionable from an extended configuration to a relaxed configuration. A first sealing portion connected to the first plurality of legs forms a sealing structure when the legs transition to the relaxed configuration to reduce perivalvular leakage between the implanted valve and surrounding tissue.