Condition monitoring of power transformers is crucial for the reliable and cost-effective operation of the power grid. The health index (HI) formulation is a pragmatic approach to combine multiple information sources and generate a consistent health state indicator for asset management planning. Generally, existing transformer HI methods are based on expert knowledge or data-driven models of specific transformer subsystems. However, the effect of uncertainty is not considered when integrating expert knowledge and data-driven models for the system-levelHI estimation. With the increased dynamic and non-deterministic engineering problems, the sources of uncertainty are increasing across power and energy applications, e.g. electric vehicles with new dynamic loads or nuclear power plants with de-energized periods, and transformer health assessment under uncertainty is becoming critical for accurate condition monitoring. In this context, this paper presents a novel soft computing driven probabilistic HI framework for transformer health monitoring. The approach encapsulates data analytics and expert knowledge along with different sources of uncertainty and infers a transformer HI value with confidence intervals for decision-making under uncertainty. Using real data from a nuclear power plant, the proposed framework is compared with traditional HI implementations and results confirm the validity of the approach for transformer health assessment.