We introduce a new construction of spherical wavelets for the unit ball, labelled as Radial 3D Needlets. We consider an experimental framework where data are collected on concentric spheres with the same pixelization at different radial distances from the origin. The unit ball is therefore viewed as a tensor product of the unit interval with the unit sphere. In the harmonic domain, a set of eigenfunctions is hence defined on the corresponding Laplacian operator. We construct these wavelets by a smooth convolution of the projectors defined by these eigenfunctions. Localization properties may be rigorously shown to hold in the real and harmonic domain, and an exact reconstruction formula holds.