Abstract Connected speech recovers to different degrees across people after left hemisphere stroke, but white matter predictors of differential recovery from the acute stage of stroke are unknown. We assessed changes in lexical–syntactic aspects of connected speech in a longitudinal analysis of 40 individuals (18 females) from the acute stage of left hemisphere stroke (within an average of 4 days post-stroke) to subacute (within 2 months) and chronic stages (early: 6 months, late: 1 year) while measuring the extent of acute lesions on white matter tracts to identify tracts predictive of recovery. We found that acute damage to the frontal aslant tract led to a decreased recovery of the fluency and structural complexity of connected speech during the year following left hemisphere stroke. The results were independent of baseline performance, overall lesion volume and the proportion of damage to tract-adjacent grey matter. This longitudinal analysis from acute to chronic stroke provides the first evidence that recovery of fluent and structurally complex spontaneous connected speech requires intact left frontal connectivity via the frontal aslant tract. That the frontal aslant tract was critical for recovery at early as well as later stages of stroke demonstrates that anterior connectivity plays a lasting and important role for the reorganization of function related to the successful production of connected speech.