A sealing system seals the perimeter of insulated hinged double doors. The sealing system includes first and second exterior seals made of a monolithic, resilient and elastically deformable material. The first exterior seal has an elongated lobe for contacting the exterior of said door, and both of the first and second exterior seals have an interior lobe which contact one another when the doors are closed. The sealing system further includes first and second inner seals made of a monolithic, resilient and elastically deformable material, each having a pair of spaced-apart sealing lobes. The inner seals are mounted to respective doors in a staggered fashion, such that the respective pairs of sealing lobes interact with one another to create a redundant, weather-resistant and thermally robust seal when the double doors are closed.