Aims: Cognitive impairment (CI) is highly prevalent in heart failure (HF), and increases patients' risks of readmission. This study sought to determine whether the presence and degree of CI could identify patients most likely to benefit from a HF disease management programme (DMP) to reduce readmissions. Methods and results: A total of 1152 consecutive Australian patients admitted with HF (2014–2017) were prospectively followed up for 12 months. Of these, 324 patients who received DMP (1-month duration, including post-discharge home visits, medication reconciliation, exercise guidance and early clinical review) were matched (1:2 ratio) with 648 usual care patients. Cognitive function was assessed either on the day of or one day before discharge using the Montreal Cognitive Assessment (MoCA). Outcomes included readmission or death at 1, 3 and 12 months, and days at home within 12 months of discharge. Poorer cognitive function was associated with all adverse outcomes. Compared with usual care, DMP was associated with lower odds of 30-day [odds ratio (OR) 0.60, 95% confidence interval 0.40, 0.91] and 90-day (OR 0.53, 95% confidence interval 0.36, 0.77) readmission or death, and with 19 more days at home within 12 months, independent of HF therapy. The effect sizes of these associations were greater for patients with diminished cognition than those with normal cognition (interaction P = 0.036), and might have been more pronounced among those with mild CI compared with those with more severe CI (MoCA score 17–22; OR 0.42, 95% confidence interval 0.21, 0.87) at 30 days (OR 0.31, 95% confidence interval 0.16, 0.60 at 90 days). Patients with normal cognition had fewer events, irrespective of DMP. Conclusions: Cognitive function may determine how HF patients respond to a DMP. Cognitive screening before implementation of a DMP may allow personalized plans for patients with different levels of cognitive function.