  We define a Fourier-Mukai transform for Higgs bundles on smooth curves and
study its properties. It is shown that the transform of a stable zero-degree
Higgs bundle is an algebraic vector bundle on the cotangent bundle of the
Jacobian of the curve. We show that this transformed bundle admits a natural
extension to an algebraic vector bundle over a projective compactification of
the base. The main result is that the original Higgs bundle can be
reconstructed from this extension. We also compute certain invariants of the
transformed bundle.
