A grounding brush assembly includes a grounding brush having a support and a plurality of conductive fibers fitted inside of the support. A brush fitting plate is connected with the support of the brush, the fitting plate including a radial portion, which is supported axially against the support, and a plurality of retention tongues for axial retention of the support. The fitting plate also includes an annular axial portion for radial centering of the support of the brush, which extends from the radial portion and is supported radially against the support of the brush. Further, the retention tongues extend from the annular axial centering portion.