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Tissue organization requires the interplay between biochemical signaling and cellular force generation. The formation of straight boundaries separating cells with different fates into compartments is important for growth and patterning during tissue development. In the developing Drosophila wing disc, maintenance of the straight anteroposterior (AP) compartment boundary involves a local increase in mechanical tension at cell bonds along the boundary. The biochemical signals that regulate mechanical tension along the AP boundary, however, remain unknown. Here, we show that a local difference in Hedgehog signal transduction activity between anterior and posterior cells is necessary and sufficient to increase mechanical tension along the AP boundary. This difference in Hedgehog signal transduction is also required to bias cell rearrangements during cell intercalations to keep the characteristic straight shape of the AP boundary. Moreover, severing cell bonds along the AP boundary does not reduce tension at neighboring bonds, implying that active mechanical tension is upregulated, cell bond by cell bond. Finally, differences in the expression of the homeodomain-containing protein Engrailed also contribute to the straight shape of the AP boundary, independently of Hedgehog signal transduction and without modulating cell bond tension. Our data reveal a novel link between local differences in Hedgehog signal transduction and a local increase in active mechanical tension of cell bonds that biases junctional rearrangements. The large-scale shape of the AP boundary thus emerges from biochemical signals inducing patterns of active tension on cell bonds.