Trans-Neptunian objects (TNOs) are remnants of a collisionally and dynamically evolved planetesimal disk in the outer solar system. This complex structure, known as the trans-Neptunian belt (or Edgeworth-Kuiper belt), can reveal important clues about disk properties, planet formation, and other evolutionary processes. In contrast to the predictions of accretion theory, TNOs exhibit surprisingly large eccentricities, e, and inclinations, i, which can be grouped into distinct dynamical classes. Several models have addressed the origin and orbital evolution of TNOs, but none has reproduced detailed observations, e.g., all dynamical classes and peculiar objects, or provided insightful predictions. Based on extensive simulations of planetesimal disks with the presence of the four giant planets and massive planetesimals, we propose that the orbital history of an outer planet with tenths of the Earth's mass can explain the trans-Neptunian belt orbital structure. This massive body was likely scattered by one of the giant planets, which then stirred the primordial planetesimal disk to the levels observed at 40-50 AU and truncated it at about 48 AU before planet migration. The outer planet later acquired an inclined stable orbit (≥100 AU; 20-40°) because of a resonant interaction with Neptune (an r:1 or r:2 resonance possibly coupled with the Kozai mechanism), guaranteeing the stability of the trans-Neptunian belt. Our model consistently reproduces the main features of each dynamical class with unprecedented detail; it also satisfies other constraints such as the current small total mass of the trans-Neptunian belt and Neptune's current orbit at 30.1 AU. We also provide observationally testable predictions.