  In this paper, Poisson wavelets on $n$-dimensional spheres, derived from
Poisson kernel, are introduced and characterized. We compute their Gegenbauer
expansion with respect to the origin of the sphere, as well as with respect to
the field source. Further, we give recursive formulae for their explicit
representations and we show how the wavelets are localized in space. Also their
Euclidean limit is calculated explicitly and its space localization is
described. We show that Poisson wavelets can be treated as wavelets derived
from approximate identities and we give two inversion formulae.
