Peculiar velocities, obtained from direct distance measurements, are data of choice to achieve constrained simulations of the Local Universe reliable down to a scale of a few Megaparsecs. Unlike redshift surveys, peculiar velocities are direct tracers of the underlying gravitational field as they trace both baryonic and dark matter. This paper presents the first attempt to use solely observational peculiar velocities to constrain cosmological simulations of the nearby universe. In order to set up Initial Conditions, a Reverse Zel'dovich Approximation (RZA) is used to displace constraints from their positions at z=0 to their precursors' locations at higher redshifts. An additional new feature replaces original observed radial peculiar velocity vectors by their full 3D reconstructions provided by the Wiener-Filter (WF) estimator. Subsequently, the Constrained Realization of Gaussian fields technique (CR) is applied to build various realizations of the Initial Conditions. The WF/RZA/CR method is first tested on realistic mock catalogs built from a reference simulation similar to the Local Universe. These mocks include errors on peculiar velocities, on data-point positions and a large continuous zone devoid of data in order to mimic galactic extinction. Large scale structures are recovered with a typical accuracy of 5 Megaparsecs/h in position, the best realizations reaching a 2-3 Mpc/h precision, the limit imposed by the RZA linear theory. Then, the method is applied to the first observational radial peculiar velocity catalog of the project Cosmicflows. This paper is a proof of concept that the WF/RZA/CR method can be applied to observational peculiar velocities to successfully build constrained Initial Conditions.