The paper develops a systematic method for renormalizing the AdS/CFT prescription to compute correlation functions. This involves regularizing the bulk on-shell supergravity action covariantly, computing all divergences, adding counterterms to cancel them, and then removing the regulator. The method is applied to pure gravity up to six dimensions and gravity coupled to scalars. The approach can also be seen as providing a holographic reconstruction of the bulk spacetime metric and fields from conformal field theory (CFT) data. Knowing which sources are turned on is sufficient to obtain an asymptotic expansion of the bulk metric and fields near the boundary, allowing for the extraction of all infrared divergences of the on-shell action. To continue the holographic reconstruction, new CFT data—specifically, the expectation value of the dual operator—are required. The paper provides explicit formulae for the holographic stress-energy tensors up to six dimensions and shows that both gravitational and matter conformal anomalies of the boundary theory are correctly reproduced. Additionally, the conformal transformation properties of the boundary stress-energy tensors are discussed. The results are organized into sections covering the Dirichlet boundary problem for AdS gravity, the holographic stress-energy tensor, conformal transformation properties, and the inclusion of matter.The paper develops a systematic method for renormalizing the AdS/CFT prescription to compute correlation functions. This involves regularizing the bulk on-shell supergravity action covariantly, computing all divergences, adding counterterms to cancel them, and then removing the regulator. The method is applied to pure gravity up to six dimensions and gravity coupled to scalars. The approach can also be seen as providing a holographic reconstruction of the bulk spacetime metric and fields from conformal field theory (CFT) data. Knowing which sources are turned on is sufficient to obtain an asymptotic expansion of the bulk metric and fields near the boundary, allowing for the extraction of all infrared divergences of the on-shell action. To continue the holographic reconstruction, new CFT data—specifically, the expectation value of the dual operator—are required. The paper provides explicit formulae for the holographic stress-energy tensors up to six dimensions and shows that both gravitational and matter conformal anomalies of the boundary theory are correctly reproduced. Additionally, the conformal transformation properties of the boundary stress-energy tensors are discussed. The results are organized into sections covering the Dirichlet boundary problem for AdS gravity, the holographic stress-energy tensor, conformal transformation properties, and the inclusion of matter.