  We provide a complete classification of Teichm\"uller curves occurring in
hyperelliptic components of the meromorphic strata of differentials. Using a
non-existence criterion based on how Teichm\"uller curves intersect the
boundary of the moduli space we derive a contradiction to the algebraicity of
any candidate outside of Hurwitz covers of strata with projective dimension one
and Hurwitz covers of zero residue loci in strata with projective dimension
two.
