We present a simple empirical function for the average density profile of cosmic voids, identified via the watershed technique in ΛCDM N -body simulations. This function is universal across void size and redshift, accurately describing a large radial range of scales around void centers with only two free parameters. In analogy to halo density profiles, these parameters describe the scale radius and the central density of voids. While we initially start with a more general four-parameter model, we find two of its parameters to be redundant, as they follow linear trends with the scale radius in two distinct regimes of the void sample, separated by its compensation scale. Assuming linear theory, we derive an analytic formula for the velocity profile of voids and find an excellent agreement with the numerical data as well. In our companion paper [Sutter et al., Mon. Not. R. Astron. Soc. 442, 462 (2014)] the presented density profile is shown to be universal even across tracer type, properly describing voids defined in halo and galaxy distributions of varying sparsity, allowing us to relate various void populations by simple rescalings. This provides a powerful framework to match theory and simulations with observational data, opening up promising perspectives to constrain competing models of cosmology and gravity. Introduction.-While tremendous effort has been conducted studying the properties of dark matter halos, cosmic voids have largely been unappreciated by the broad scientific community. However, as voids occupy the most underdense regions in the Universe, and constitute the dominant volume fraction of it, they are promising independent probes to test our theories of structure formation and cosmology. For example, voids are the ideal laboratories for studies of dark energy (e.g., Refs. [1-5]) and modified gravity (e.g., Refs. [6-9]), as the importance of ordinary gravitating matter is mitigated in their interior. Unlike dark matter halos, voids are in addition more closely related to the initial conditions of the Universe, thanks to the limited number of phase-space foldings occurring inside of them [10][11][12][13][14][15].A fundamental quantity to describe the structure of voids in a statistical sense is their spherically averaged density profile. In contrast to the well-known formulas parametrizing density profiles of simulated dark matter halos (e.g., Refs. [16][17][18][19]), rather few models for void density profiles have been developed, mainly focusing on the central regions [3,[20][21][22][23], rarely taking into account the compensation walls outside the void [24]. In this Letter we present a simple formula that is able to accurately describe the density profile around voids of any size and redshift, out to large distances from their center. Although we focus our attention on dark matter simulations here, our companion paper [25] extends the analysis to voids defined in other tracer types, such as dark matter halos and mock galaxies of various number densities, yielding consistent results. Thus, give...