Unsupervised anomaly detection (AD) is critical for a wide range of practical applications, from network security to health and medical tools. Due to the diversity of problems, no single algorithm has been found to be superior for all AD tasks. Choosing an algorithm, otherwise known as the Algorithm Selection Problem (ASP), has been extensively examined in supervised classification problems, through the use of meta-learning and AutoML, however, it has received little attention in unsupervised AD tasks. This research proposes a new meta-learning approach that identifies an appropriate unsupervised AD algorithm given a set of meta-features generated from the unlabelled input dataset. The performance of the proposed meta-learner is superior to the current state of the art solution. In addition, a mixed model statistical analysis has been conducted to examine the impact of the meta-learner components: the meta-model, meta-features, and the base set of AD algorithms, on the overall performance of the meta-learner. The analysis was conducted using more than 10,000 datasets, which is significantly larger than previous studies. Results indicate that a relatively small number of meta-features can be used to identify an appropriate AD algorithm, but the choice of a meta-model in the meta-learner has a considerable impact