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Objectives The aim of the study was to assess the rates of discontinuation of integrase inhibitor regimens because of any neuropsychiatric adverse event (NPAE) and the factors associated with discontinuation. Methods A population‐based, prospective, multicentre cohort study was carried out. Treatment‐naïve subjects starting therapy with a regimen containing integrase inhibitors, or those switching to such a regimen, with plasma HIV‐1 RNA < 50 HIV‐1 RNA copies/mL in 14 hospitals in Catalonia or the Balearic Islands (Spain) were included in the study. Every discontinuation because of adverse events (AEs) was double‐checked directly with treating physicians. Multivariable Cox models identified factors correlated with discontinuation. Results A total of 4165 subjects (37% treatment‐naïve) started regimens containing dolutegravir (n = 1650; 91% with abacavir), raltegravir (n = 930) or elvitegravir/cobicistat (n = 1585). There were no significant differences among regimens in the rate of discontinuation because of any AE. Rates of discontinuation because of NPAEs were low but higher for dolutegravir/abacavir/lamivudine [2.1%; 2.9 (95% confidence interval (CI) 2.0, 4.2) discontinuations/100 patients/year] versus elvitegravir/cobicistat (0.5%; 0.8 (95% CI 0.3, 1.5) discontinuations/100 patients/year], with significant differences among centres for dolutegravir/abacavir/lamivudine and NPAEs (P = 0.003). We identified an association of female gender and lower CD4 count with increased risk of discontinuation because of any AE [Incidence ratio (IR) 2.3 (95% CI 1.4, 4.0) and 1.8 (95% CI 1.1, 2.8), respectively]. Female gender, age > 60 years and abacavir use were not associated with NPAE discontinuations. NPAEs were commonly grade 1–2, and had been present before and improved after drug withdrawal. Conclusions In this large prospective cohort study, patients receiving dolutegravir, raltegravir or elvitegravir/cobicistat did not show significant differences in the rate of discontinuation because of any toxicity. The rate of discontinuations because of NPAEs was low, but was significantly higher for dolutegravir than for elvitegravir/cobicistat, with significant differences among centres, suggesting that greater predisposition to believe that a given adverse event is caused by a given drug of some treating physicians might play a role in the discordance seen between cohorts.