Despite constant efforts of organisations to ensure a fair and transparent personnel selection process, hiring is still characterised by systematic inequality. The potential of algorithms to produce fair and objective decision outcomes has attracted the attention of academic scholars and practitioners as a conceivable alternative to human decision-making. However, applicants do not necessarily consider an objective algorithm as fairer than a human decision maker. This study examines the conditions under which applicants perceive algorithms as fair and establishes a theoretical foundation of algorithmic fairness perceptions. We further propose and investigate transparency and anthropomorphism interventions as strategies to actively shape these fairness perceptions. In an online application scenario with eight experimental groups (N = 801), we analyse determinants for algorithmic fairness perceptions and the impact of the proposed interventions. Embedded in a stimulus- organism-response framework and drawing from organisational justice theory, our study reveals four justice dimensions (procedural, distributive, interpersonal, informational justice) that determine algorithmic fairness perceptions. The results further show that transparency and anthropomorphism interventions mainly affect dimensions of interpersonal and informational justice, highlighting the importance of algorithmic fairness perceptions as critical determinants for individual choices.