Fedotovite K_{2}Cu_{3}O(SO_{4})_{3} is a candidate of new quantum spin systems, in which the edge-shared tetrahedral (EST) spin clusters consisting of Cu^{2+} are connected by weak intercluster couplings forming a one-dimensional array. Comprehensive experimental studies by magnetic susceptibility, magnetization, heat capacity, and inelastic neutron scattering measurements reveal the presence of an effective S=1 Haldane state below T≅4 K. Rigorous theoretical studies provide an insight into the magnetic state of K_{2}Cu_{3}O(SO_{4})_{3}: an EST cluster makes a triplet in the ground state and a one-dimensional chain of the EST induces a cluster-based Haldane state. We predict that the cluster-based Haldane state emerges whenever the number of tetrahedra in the EST is even.