Cellobiohydrolases are exo-acting, processive enzymes, which effectively hydrolyze crystalline cellulose. They have attracted considerable interest due to their role in both in natural carbon cycling and industrial enzyme cocktails used for the deconstruction of cellulosic biomass, but many mechanistic and regulatory aspects of their heterogeneous catalysis remain poorly understood. Here we address this by applying a deterministic model to real-time kinetic data with high temporal resolution. We used two variants of the cellobiohydrolase Cel7A from H. jecorina, and three types of cellulose as substrate. Analysis of the pre-steady state regime allowed delineation rate constants for both fast and slow steps in the enzymatic cycle and assessment of how these constants influenced the rate of hydrolysis at quasi-steady state. Processive movement on the cellulose strand advanced with characteristic times of 0.15 - 0.7 s per step at 25 °C, and the rate was highest on amorphous substrate. The cellulose binding module (CBM) was found to raise this rate on crystalline, but not on amorphous substrate. The rapid processive movement signified high intrinsic reactivity, but this parameter had marginal influence on the steady state rate. This was because dissociation and association were slower and hence rate limiting. Specifically, the dissociation from the strand was found to occur with characteristic times of 45-100 s. This meant that dissociation was the bottleneck, except at very low substrate loads (0.5 – 1 g/l) where association became slower.