Let \(M = G/H\) be a homogeneous Riemannian manifold and \(\mu\) a fixed isometry of \(M\) such that \(\mu G \mu^{-1} = G\) and \(\mu^2 \in G\). The space \(M\) is called weakly symmetric if for any points \(x\) and \(y\) in \(M\) there exists a \(g \in G\) such that \(gx = \mu y, gy = \mu x\). A symmetric space is thus weakly symmetric. A. Selberg proved in [J. Indian Math. Soc. 20, 47-87 (1956; Zbl 0072.08201)] that if \(M\) is weakly symmetric then the algebra of all \(G\)-invariant differential operators on \(M\) is commutative, consequently \((G, H)\) is a spherical pair, namely every unitary irreducible representation of \(G\) contains at most one \(H\)-fixed vector. The converse is, however, proved not true by J. Lauret [Bull. Lond. Math. Soc. 30, No. 1, 29-36 (1998; Zbl 0921.22007)]. In the present paper the author proves that if \((G, H)\) is a compact spherical pair with \(G\) being a compact semisimple Lie group, then \(G/H\) is weakly symmetric. The proof is done through a case-by-case check of the classification of compact spherical pairs \((G, H)\) by M. Krämer [Compos. Math. 38, No. 2, 129-153 (1979; Zbl 0402.22006)].