Sign languages are naturally occurring languages. As such, their emergence and spread reflect the histories of their communities. However, limitations in historical recordkeeping and linguistic documentation have hindered the diachronic analysis of sign languages. In this work, we used computational phylogenetic methods to study family structure among 19 sign languages from deaf communities worldwide. We used phonologically coded lexical data from contemporary languages to infer relatedness and suggest that these methods can help study regular form changes in sign languages. The inferred trees are consistent in key respects with known historical information but challenge certain assumed groupings and surpass analyses made available by traditional methods. Moreover, the phylogenetic inferences are not reducible to geographic distribution but do affirm the importance of geopolitical forces in the histories of human languages.