Abstract. Using a new compactification of the (braid) configuration space of $n$ points in the upper half plane we construct explicitly a universal homotopy action of the Grothendieck-Teichmueller group on the set Poisson structures in an arbitrary affine space. It is also shown that, for any affine supermanifold $M$ equipped with a constant odd symplectic structure, there is a universal homotopy action of the Grothendieck-Teichmueller group on the set of quantum BV structures on $M$.