Fastened to a tire is a detecting device consisting of a detecting unit including a sensor associated with an annular antenna having an inner perimetral edge, and an anchoring body having a base portion with a fastening surface secured to the radially internal surface of the tire. The detecting unit is removably brought into engagement with the anchoring body by insertion of the inner perimetral edge of the antenna into a perimetral groove formed between the base portion and a retaining portion. The anchoring body has an overall height of about 0.2 to about 1.5 times a maximum distance measure between two mutually spaced apart points along the inner perimetral edge.