We investigated the origin and formation mechanisms of the intracluster light (ICL) in THE THREE HUNDRED simulations, a set of 324 hydrodynamically resimulated massive galaxy clusters. The ICL, a diffuse component comprised of stars not bound to any individual galaxy, serves as a critical tracer of cluster formation and evolution. Using two implementations of hydrodynamics, GADGET-X and GIZMO-SIMBA, we identified the stellar particles that constitute the ICL at z = 0 and traced them back in time to the moments when they were formed and accreted into the ICL. Our analysis reveals that, across our 324 clusters, half of the present-day ICL mass is typically in place between z ∼ 0.2 and 0.5. The main ICL formation channel is the stripping of stars from subhalos after their infall into the host cluster. Within this channel, 65−80% of the ICL comes from objects with stellar (infall) masses above 1011 M⊙, corresponding to massive galaxies, groups and clusters. When we also consider the ratio of the infalling halo to the total cluster mass, we see that a median of 35% of the mass is brought in major merger events, although the percentage varies significantly across clusters (15−55%). Additional contributions come from minor mergers (25−35%) and smooth accretion (20−50%). The infall redshift of the primary contributors is generally below z ≤ 1, with smaller fractions arriving at redshifts between 1 and 2. Regarding other formation channels, we find minor contributions from stars formed in subhalos after their infall and stars stripped while their contributing halo remains outside the host cluster (and can eventually fall inside or stay outside). Finally, for our two sets of simulations, we find medians of 12 (GADGET-X) and 2 (GIZMO-SIMBA) percent of the ICL mass formed in situ, i.e. directly as part of the diffuse component. However, this component can be attributed to stripping of gas in high-velocity infalling satellite galaxies.