We present FAST, an optimization framework for fast additive segmentation. FAST segments piecewise constant shape functions for each feature in a dataset to produce transparent additive models. The framework leverages a novel optimization procedure to fit these models $\sim$2 orders of magnitude faster than existing state-of-the-art methods, such as explainable boosting machines \citep{nori2019interpretml}. We also develop new feature selection algorithms in the FAST framework to fit parsimonious models that perform well. Through experiments and case studies, we show that FAST improves the computational efficiency and interpretability of additive models.