Pulsating variable stars are invaluable tracers for reconstructing the star formation history and chemical evolution of their host galaxies. In this work, we explore the variable star population of Leo II, a distant dwarf spheroidal satellite of the Milky Way. We analyse an extensive dataset of ground-based BVRI time-series photometry spanning over 35 years. By examining the properties of RR Lyrae stars, we constrain the early chemical enrichment and spatial variation within Leo II. Additionally, we investigate the anomalous Cepheids in order to connect their characteristics with the galaxy's prolonged star formation history, as revealed by deep HST/WFC3 colour-magnitude diagrams. We identified and characterised 175 variable stars, with all but one associated with Leo~II. Our work includes the discovery of 25 new RR Lyrae stars and two new anomalous Cepheids. Moreover, we reclassified V88 as a BL Her variable star. By employing multiple independent methods, including metallicity-luminosity relations for RR Lyrae stars and period-luminosity and period-Wesenheit relations for both RR Lyrae and anomalous Cepheids, we derived a true distance modulus of (m-M)_0=21.60+/-0.03mag, corresponding to 209+/-4kpc. Furthermore, we discuss potential formation scenarios for anomalous Cepheids and suggest that, despite the extended star formation history, they are all compatible having originated from old binary stars, with no contribution from young, evolved single stars.