Background: Previous studies have highlighted a relationship between reduction in rate of exacerbations with therapies containing inhaled corticosteroids (ICS) and baseline blood eosinophil count in patients with chronic obstructive pulmonary disease (COPD). The IMPACT trial showed that once-daily single-inhaler triple therapy significantly reduced exacerbations versus dual therapies. Blood eosinophil counts and smoking status could be important modifiers of treatment response to ICS. We aimed to model these relationships and their interactions, including outcomes other than exacerbations. Methods: IMPACT was a phase 3, randomised, double-blind, parallel-group, 52-week global study comparing once-daily single-inhaler triple therapy (fluticasone furoate–umeclidinium–vilanterol) with dual inhaled therapy (fluticasone furoate–vilanterol or umeclidinium–vilanterol). Eligible patients had moderate-to-very-severe COPD and at least one moderate or severe exacerbation in the previous year. We used fractional polynomials to model continuous blood eosinophil counts. We used negative binomial regression for numbers of moderate and severe exacerbations, severe exacerbations, and pneumonia. We modelled differences at week 52 in trough FEV1, St George's Respiratory Questionnaire (SGRQ) total score, and Transition Dyspnoea Index using repeated measurements mixed effect models. IMPACT was registered with ClinicalTrials.gov, number NCT02164513. Findings: The magnitude of benefit of regimens containing ICS (fluticasone furoate–umeclidinium–vilanterol n=4151 and fluticasone furoate–vilanterol n=4134) in reducing rates of moderate and severe exacerbations increased in proportion with blood eosinophil count, compared with a non-ICS dual long-acting bronchodilator (umeclidinium–vilanterol n=2070). The moderate and severe exacerbation rate ratio for triple therapy versus umeclidinium–vilanterol was 0·88 (95% CI 0·74 to 1·04) at blood eosinophil count less than 90 cells per μL and 0·56 (0·47 to 0·66) at counts of 310 cells per μL or more; the corresponding rate ratio for fluticasone furoate–vilanterol versus umeclidinium–vilanterol was 1·09 (0·91 to 1·29) and 0·56 (0·47 to 0·66), respectively. Similar results were observed for FEV1, Transition Dyspnoea Index, and SGRQ total score; however, the relationship with FEV1 was less marked. At blood eosinophil counts less than 90 cells per μL and at counts of 310 cells per μL or more, the triple therapy versus umeclidinium–vilanterol treatment difference was 40 mL (95% CI 10 to 70) and 60 mL (20 to 100) for trough FEV1, −0·01 (–0·68 to 0·66) and 0·30 (–0·37 to 0·97) for Transition Dyspnoea Index score, and −0·01 (–1·81 to 1·78) and −2·78 (–4·64 to −0·92) for SGRQ total score, respectively. Smoking status modified the relationship between observed efficacy and blood eosinophil count for moderate or severe exacerbations, Transition Dyspnoea Index, and FEV1, with former smokers being more corticosteroid responsive at any eosinophil count than current smokers. Interpretation: This analysis of the IMPACT trial shows that assessment of blood eosinophil count and smoking status has the potential to optimise ICS use in clinical practice in patients with COPD and a history of exacerbations. Funding: GlaxoSmithKline.