Background: Patients with asthma who are inadequately controlled on inhaled corticosteroid–long-acting β2-adrenoceptor agonist (ICS–LABA) combinations might benefit from the addition of a long-acting muscarinic receptor antagonist. The aim of the IRIDIUM study was to assess the efficacy and safety of a once-daily, single-inhaler combination of mometasone furoate, indacaterol acetate, and glycopyrronium bromide (MF–IND–GLY) versus ICS–LABA in patients with inadequately controlled asthma. Methods: In this 52-week, double-blind, double-dummy, parallel-group, active-controlled phase 3 study, patients were recruited from 415 sites across 41 countries. Patients aged 18 to 75 years with symptomatic asthma despite treatment with medium-dose or high-dose ICS–LABA, at least one exacerbation in the previous year, and a percentage of predicted FEV1 of less than 80% were included. Enrolled patients were randomly assigned (1:1:1:1:1) via interactive response technology to receive medium-dose or high-dose MF–IND–GLY (80 μg, 150 μg, 50 μg; 160 μg, 150 μg, 50 μg) or MF–IND (160 μg, 150 μg; 320 μg, 150 μg) once daily via Breezhaler, or high-dose fluticasone–salmeterol (FLU–SAL; 500 μg, 50 μg) twice daily via Diskus. The primary outcome was change from baseline in trough FEV1 with MF–IND–GLY versus MF–IND at week 26 in patients in the full analysis set, analysed by means of a mixed model for repeated measures. Safety was assessed in all patients who received at least one dose of study drug. This study is registered with ClinicalTrials.gov, NCT02571777, and is completed. Findings: Between Dec 8, 2015, and Jun 14, 2019, 3092 of 4851 patients screened were randomly assigned (medium-dose MF–IND–GLY, n=620; high-dose MF–IND–GLY, n=619; medium-dose MF–IND, n=617; high-dose MF–IND, n=618; high-dose FLU–SAL, n=618). 2747 (88·8%) patients completed the 52-week treatment and 321 (10·4%) started but discontinued study treatment prematurely. Medium-dose MF–IND–GLY (treatment difference [Δ] 76 mL [95% CI 41–111]; p<0·001) and high-dose MF–IND–GLY (Δ 65 mL [31–99]; p<0·001) showed superior improvement in trough FEV1 versus corresponding doses of MF–IND at week 26. Improvements in trough FEV1 were greater for both medium-dose MF–IND–GLY (99 mL [64–133]; p<0·001) and high-dose MF–IND–GLY (119 mL [85–154]; p<0·001) than for high-dose FLU–SAL at week 26. Overall, the incidence of adverse events was balanced across the treatment groups. Seven deaths were reported (one with medium-dose MF–IND–GLY, two with high-dose MF–IND–GLY, and four with high-dose MF–IND) during the study; none of these deaths was considered by the investigators to be caused by study drugs or other study-related factors. Interpretation: Once-daily, single-inhaler MF–IND–GLY improved lung function versus ICS–LABA combinations (MF–IND and FLU–SAL) in patients with inadequately controlled asthma. The safety profile was similar across treatment groups. MF–IND–GLY therefore constitutes a good treatment option in these patients. Funding: Novartis Pharmaceuticals.