Abstract The first discovered extrasolar worlds—giant, “hot Jupiter” planets on short-period orbits—came as a surprise to solar system–centric models of planet formation, prompting the development of new theories for planetary system evolution. The near absence of observed nearby planetary companions to hot Jupiters has been widely quoted as evidence in support of high-eccentricity tidal migration, a framework in which hot Jupiters form further out in their natal protoplanetary disks before being thrown inward with extremely high eccentricities, stripping systems of any close-in planetary companions. In this work, we present new results from a search for transit timing variations across the full 4 yr Kepler data set, demonstrating that at least 12% ± 6% of hot Jupiters have a nearby planetary companion. This subset of hot Jupiters is expected to have a quiescent dynamical history such that the systems could retain their nearby companions. We also demonstrate a ubiquity of nearby planetary companions to warm Jupiters (≥70% ± 16%), indicating that warm Jupiters typically form quiescently. We conclude by combining our results with existing observational constraints to propose an “eccentric migration” framework for the formation of short-period giant planets through postdisk dynamical sculpting in compact multiplanet systems. Our framework suggests that hot Jupiters constitute the natural end stage for giant planets spanning a wide range of eccentricities, with orbits that reach small enough periapses—either from their final orbital configurations in the disk phase or from eccentricity excitation in the postdisk phase—to trigger efficient tidal circularization.