Background and Objective: Numerical simulations of blood flow are a valuable tool to investigate the pathophysiology of ascending thoratic aortic aneurysms (ATAA). To accurately reproduce in vivo hemodynamics, computational fluid dynamics (CFD) models must employ realistic inflow boundary conditions (BCs). However, the limited availability of in vivo velocity measurements, still makes researchers resort to idealized BCs. The aim of this study was to generate and thoroughly characterize a large dataset of synthetic 4D aortic velocity profiles sampled on a 2D cross-section along the ascending aorta with features similar to clinical cohorts of patients with ATAA. Methods: Time-resolved 3D phase contrast magnetic resonance (4D flow MRI) scans of 30 subjects with ATAA were processed through in-house code to extract anatomically consistent cross-sectional planes along the ascending aorta, ensuring spatial alignment among all planes and interpolating all velocity fields to a reference configuration. Velocity profiles of the clinical cohort were extensively characterized by computing flow morphology descriptors of both spatial and temporal features. By exploiting principal component analysis (PCA), a statistical shape model (SSM) of 4D aortic velocity profiles was built and a dataset of 437 synthetic cases with realistic properties was generated. Results: Comparison between clinical and synthetic datasets showed that the synthetic data presented similar characteristics as the clinical population in terms of key morphological parameters. The average velocity profile qualitatively resembled a parabolic-shaped profile, but was quantitatively characterized by more complex flow patterns which an idealized profile would not replicate. Statistically significant correlations were found between PCA principal modes of variation and flow descriptors. Conclusions: We built a data-driven generative model of 4D aortic inlet velocity profiles, suitable to be used in computational studies of blood flow. The proposed software system also allows to map any of the generated velocity profiles to the inlet plane of any virtual subject given its coordinate set.