Virtual influencer marketing is an emerging research area due to the increasing popularity of virtual influencers across the social media landscape. However, existing literature falls short when it comes to explaining how consumers perceive the attributes of virtual influencers and what their roles are in determining the cognitive acceptance of the messages they communicate. To address the research gaps, this study pursued the objective of exploring the cognitive processes of individuals being exposed to the information elicited by virtual influencers. We adopted Social Influence Theory, which postulates that there are three processes of influence acceptance, namely compliance, internalisation and identification, each of which is conditioned by a set of different factors. To address the research objective, this study was carried out in two stages. In the first exploratory stage, we drew on relevant research to identify the attributes of virtual influencers, which could predict the three influence acceptance processes. To ensure the accuracy of the results, three approaches to the validation and filtering of attributes were used, i.e.: a quantitative and qualitative content analysis of 126 papers discussing the characteristics of influencers and a survey-based ranking of the importance of the generated attributes. As a result, we found that the top 8 statistically significant factors are warmth, relatedness, interactivity, competence, empathy, uniqueness, fairness and credibility. In the second stage, based on a sample of 601 respondents, we analysed the associations of the identified attributes with cognitive processes using a fuzzy-set qualitative comparative analysis (fsQCA). The analysis showed different configurations of the core and peripheral predictors of compliance, identification and internalisation. For a high level of compliance, a high level of interactivity is a core condition; for a high level of identification, empathy, competence, fairness, interactivity, and credibility act as core predictors. A high level of internalisation is associated with two core predictors, namely interactivity and relatedness. The findings of the study contribute to the extant literature on virtual influencers by providing empirical evidence about the cognitive acceptance of influence elicited by virtual influencers and the characteristics of non-human opinion leaders that shape consumers’ attitudes and behaviour. The findings offer practical insights into how to enhance the persuasiveness of virtual influencers’ messages.