In recent years, the transition to clean bus fleets has accelerated. Although this transition might bring environmental and economic benefits, it requires a long-term strategic plan due to the large investment costs involved. This paper proposes a multi-stage stochastic program to optimize strategic plans for the clean bus fleet transition that explicitly considers the uncertainty scenarios in the cost and efficiency improvements of clean buses. Our optimization model minimizes the total expected cost subject to emission targets, budget restrictions and several other operational considerations. We propose a new forecasting approach that captures the correlation between these improvements to obtain realistic future pathways for Battery Electric Buses (BEBs) and Hydrogen Fuel Cell Buses (HFCBs), which are then given to the multi-stage stochastic program as scenarios. We also utilize a physics-based model for BEBs to accurately capture their energy consumption and recharging needs. As a case study, we focus on the complex public bus network of Istanbul, which aims to transition to a clean bus fleet by 2050. Utilizing real datasets, we solve a five-stage stochastic program spanning a 25-year planning horizon that involves 256 scenarios to obtain dynamic strategic plans that can be used by the policy makers. Our results suggest that BEBs are more advantageous than HFCBs, even in slow BEB but fast HFCB development scenarios. We also conduct several sensitivity analyses to understand the effects of the intermediate emission targets, budget limitations and energy prices.