JARABLUS, Syria—Not far from the square here where Islamic State executioners carried out public beheadings, Syrian rebels have raised a banner trumpeting the beginning of a new era: “Welcome: #safehaventurkey”

Until late August this border town served as a strategic gateway for foreign fighters and supplies for Islamic State’s self-declared, now-shrinking caliphate. Now it is the cornerstone of Turkish President Recep Tayyip Erdogan’s plan—viewed warily by the U.S.—to transform a vast stretch of northern Syria into a haven...