Structural health prognostics can be broadly applied to various engineered artifacts in an engineered system. However, techniques and methodologies for health prognostics become application-specific. This study thus aims at formulating a generic framework of structural health prognostics, which is composed of four core elements: (i) a generic health index system with synthesized health index (SHI), (ii) a generic offline learning scheme using the sparse Bayes learning (SBL) technique, (iii) a generic online prediction scheme using the similarity-based interpolation (SBI), and (iv) an uncertainty propagation map for the prognostic uncertainty management. The SHI enables the use of heterogeneous sensory signals; the sparseness feature employing only a few neighboring kernel functions enables the real-time prediction of remaining useful lives (RULs) regardless of data size; the SBI predicts the RULs with the background health knowledge obtained under uncertain manufacturing and operation conditions; and the uncertainty propagation map enables the predicted RULs to be loaded with their statistical characteristics. The proposed generic framework of structural health prognostics is thus applicable to different engineered systems and its effectiveness is demonstrated with two cases studies.