The bearing assembly includes a rolling bearing including a rotatable raceway member and a stationary raceway member. This bearing assembly also includes a to-be-detected member carried by the raceway member and having a magnetic characteristic which cyclically varies in a direction circumferentially of the to-be-detected element and has a cycle matching with one complete rotation of the raceway member, a magnetic sensor unit carried by the raceway member in face-to-face relation with the to-be-detected member, and a magnetic detecting circuit to supply an electric power to the unit and to process an output signal from the unit to provide an output to an external circuit. The magnetic characteristic of the to-be-detected member represents a substantially sinusoidal waveform rising and falling more steeply than a sinusoidal waveform at a zero-crossing point.