Site-specific streamflow forecasting is essential to provide adequate information for early proactive water management and planning. Climate change significantly impacts streamflow variability and amounts; therefore, it should be considered in streamflow modeling. Streamflow time series comprises a lot of randomness and uncertainties, which implies that probabilistic models can be suitable for streamflow forecasting. In this study, we aim to forecast long-term streamflow (i.e., for a period ranging from a few weeks to years) using a Markov Chain model with the Chapman-Kolmogorov approach and accounting for climate change impact. The model is applied to over 100 years of monthly streamflow data from a long-recording hydrometric station in Ontario. Since climate change impact varies with seasons over the years, the proposed model was applied on the twelve months of the year using monthly streamflow to project data for a similar month after one year and five years. The historical data were categorized into five ranges of monthly streamflow values. Then, the probability of occurrence of streamflow within each category was estimated. The results showed that the developed model can adequately evaluate the probability of occurrence for different monthly flow values for more than one year ahead of the forecast. The proposed model can be used to provide a good overview of the probability of the increase or decrease in streamflow for each month based on the streamflow records of the selected location, and it has the potential to be applied in other locations.