Strategic asset management of transformer fleets in electrical power systems is a critical aspect for distribution utilities. In this study, an integrated framework for multicriteria asset management is presented. A multiobjective optimisation model is deployed, simultaneously minimising the maintenance costs and the predicted cost of unexpected failures, based on statistical estimates of failure probability and on the expected economic impact of failures. A multicriteria decision-support system is used for the selection of the recommended maintenance policy for a given time window. A criticality score for each transformer, which can assist planning engineers in defining replacement investments, is also provided. The application of the proposed framework is illustrated using the database of Brazilian power distribution utility CEMIG.