A rolling bearing device comprises an outer ring 105 provided with an internal raceway 106 formed on its bore, an inner ring 101 provided with an external raceway 102 formed on its cylindrical exterior surface, at least one row of rolling bodies 111 arranged between the two raceways 102, 106 and at least one sealing member 121 secured to one of the rings. The sealing member 121 comprises an annular metal reinforcement 123. The device comprises a part 126 for connecting between the reinforcement 123 and the ring which supports it, the connecting part 126 being formed by a filler metal which, after melting and cooling, provides attachment, sealing and molds to the shapes of the said reinforcement and the said ring.