In salamanders, grafting of a left limb blastema onto a right limb stump yields regeneration of three limbs, the normal limb and two 'supernumerary' limbs. This experiment and other research have shown that the juxtaposition of anterior and posterior limb tissue plus innervation are necessary and sufficient to induce complete limb regeneration in salamanders. However, the cellular and molecular basis of the requirement for anterior-posterior tissue interactions were unknown. Here we have clarified the molecular basis of the requirement for both anterior and posterior tissue during limb regeneration and supernumerary limb formation in axolotls (Ambystoma mexicanum). We show that the two tissues provide complementary cross-inductive signals that are required for limb outgrowth. A blastema composed solely of anterior tissue normally regresses rather than forming a limb, but activation of hedgehog (HH) signalling was sufficient to drive regeneration of an anterior blastema to completion owing to its ability to maintain fibroblast growth factor (FGF) expression, the key signalling activity responsible for blastema outgrowth. In blastemas composed solely of posterior tissue, HH signalling was not sufficient to drive regeneration; however, ectopic expression of FGF8 together with endogenous HH signalling was sufficient. In axolotls, FGF8 is expressed only in the anterior mesenchyme and maintenance of its expression depends on sonic hedgehog (SHH) signalling from posterior tissue. Together, our findings identify key anteriorly and posteriorly localized signals that promote limb regeneration and show that these single factors are sufficient to drive non-regenerating blastemas to complete regeneration with full elaboration of skeletal elements.