A ball bearing for the hub (4) of a vehicle wheel comprises a dual set of bearing balls in angular contact wherein the inner race of the axially innermost set (5) of bearing balls consists of an annular member (6) fitted onto the hub (4). The annular member (6) is secured to the hub (4) by a welding (11) performed between the axially inner end portion (14) of the hub (4) and the annular member (6) or a washer (10) adjacent thereto. At least one of the two welded parts has a low carbon content portion at the welding zone.