The invention refers to a device for sealing an annular space formed between an outer cylindrical element (4) having an end closure (16) and an inner pipe (1) extending within the outer element and having a free end. The invention incorporates a packer element (2) being slidably disposed around said pipe (1), an actuation element (6) adapted for telescopic assembly around the outer surface of the pipe (1) and slidable from a first position to a second position, a conical ring (12) adapted for installation on the pipe (1), where the actuation element (6) comprises an abutment element (10) designed for abutment against said packer (2), and an actuation pipe (8) extending beyond the pipe (1) first end when the actuation element (6) is in said first position. The invention also refers to a method for sealing the annular space.