This paper studies how transformers handle non-stationary sequences with abrupt regime changes, formalizing the problem as in-context change-point detection. The authors provide constructive theory showing that transformers can approximate the Bayesian model-averaged predictor for piecewise-linear tasks, with model complexity (depth, width, attention heads) depending on the level of side information about the change point. Specifically, knowing the exact change point reduces the candidate set size and thus the required attention heads, while partial information (e.g., support) requires more heads. Synthetic experiments on linear regression and linear dynamical systems confirm that trained transformers match optimal baselines (oracle least-squares when informed, BMA when uninformed). Real-world experiments on infectious disease forecasting (with policy changes) and financial volatility forecasting (around FOMC announcements) show that encoding change-point information via positional encoding improves pretrained foundation model performance without retraining, with up to 25% MAE reduction in disease forecasting. The work bridges classical change-point detection and modern in-context learning, offering practical methods for deploying transformers in non-stationary environments.