We present the exact Bethe Ansatz solution of a multichannel model of one- dimensional correlated electrons coupled antiferromagnetically to a magnetic impurity of arbitrary spin S. The solution reveals that interactions in the bulk make the magnetic impurity drive both spin and charge fluctuations, producing a mixed valence at the impurity site, with an associated effective spin S_eff > S in the presence of a magnetic field. The screening of the impurity spin is controlled by its size independently of the number of channels, in contrast to the multichannel Kondo effect for free electrons.