Magnetic vortices in individual nanoparticles are fundamental spin structures that govern the properties of next-generation magnetic devices and biomedical applications. However, directly imaging their complete structure, from the circulating in-plane magnetization to the nanometer scale out-of-plane core, remains challenging. Here, direct and quantitative visualization of magnetic vortex structures in individual cobalt nanoparticles is achieved by integrating a time-reversal methodology with tilt-scan-averaged differential phase contrast scanning transmission electron microscopy in a magnetic-field-free environment. This approach enables magnetic imaging in conjunction with atomic-scale analysis and reveals a correlation between particle geometry and internal demagnetizing fields. In addition, dynamic evolution of the vortex under in situ magnetic-field application is tracked, enabling unambiguous determination of the out-of-plane core polarity. This approach provides a powerful platform for correlating atomic-scale structure and magnetism within individual nanoparticles and for understanding the origins of nanoscale magnetic properties, thereby supporting the rational design of advanced nanomagnetic materials and devices.