Orientation: Engaged employees make a valuable contribution to organisational agility and productivity in challenging business environments. Hence, identifying factors that enhance employee engagement is important in the Nigerian context. Research purpose: The objectives of this study were to show that various leadership styles have different effects on employee engagement, and that the employee voice and the perception of organisational support are boundary variables through which leadership style affects employee engagement. Motivation for the study: High unemployment rate and job insecurity in Nigeria make it necessary to determine leadership styles and other factors that enhance employee engagement. Research design, approach and method: Cross-sectional survey design was used with samples taken from organisations located in Lagos, Nigeria (n = 300). Existing measures of study variables that have been validated were used for the study. Statistical Package for the Social Sciences (SPSS) and structural equation modelling techniques were used for data analysis. Main findings: The relationship between leadership style and employee engagement is not direct but mediated through boundary variables, employee voice and perception of organisational support. Servant leadership style has the highest total effect on employee engagement. Autocratic style is detrimental to the engagement of employees. Encouraging employee voice enhances the employee’s perception of the organisation as supportive. Practical/managerial implications: Though leadership is known to be the main driver of employee engagement, not all leadership styles enhance employee engagement. The effect of leadership on employee engagement is influenced by the favourable environment created by the leader’s behaviour. Organisations must use the determination of potential leadership style as recruitment tool for new managers and those to be promoted. The performance evaluation of leaders must include behavioural factors that capture leaders’ ability to create a favourable environment that encourages the employee voice and perception of organisation as supportive. Contribution/value-add: Leadership styles are not equally effective in enhancing employee engagement. There are boundary variables arising from the environment created by leadership behaviour that enhance the effect of leadership style on employee engagement. The study was performed in Nigeria where high unemployment rate and job insecurity created a unique challenge in getting employees engaged.