Let \(M= G/H\) be a homogeneous effective space with connected Lie group \(G\) and compact \(H\). It is proved that \(M\) admits a \(G\)-invariant Riemannian metric of positive Ricci curvature if and only if \(M\) is compact and its fundamental group is finite. This is equivalent to the condition that the semisimple Levi component of \(G\) is compact and acts on \(M\) transitively. Any normal metric on \(M\) has positive Ricci curvature in this case. If \(G\) is not semisimple then \(M\) can be realized as total space of a \(G\)-invariant principal bundle whose base \(B\) is the orbit space of the center of \(G\). Moreover, \(B\) is equipped in a natural way with a normal invariant Riemannian metric of positive Ricci curvature in such a way that the projection \(M\to B\) is a submersion.