Context. During protostellar collapse, conservation of angular momentum leads to the formation of an accretion disc. Little is known observationally about how and when the velocity field around the protostar shifts from infall-dominated to rotation-dominated. Aims. We investigate this transition in the low-mass protostar L1489 IRS, which is known to be embedded in a flattened, disc-like structure that shows both infall and rotation. We aim to accurately characterise the structure and composition of the envelope and its velocity field, and find clues to its nature. Methods. We construct a model for L1489 IRS consisting of an flattened envelope and a velocity field that can vary from pure infall to pure rotation. We obtain best-fit parameters by comparison to 24 molecular transitions from the literature, and using a molecular excitation code and a Voronoi optimisation algorithm. We test the model against existing millimeter interferometric observations, near-infrared scattered light imaging, and ¹²CO ro-vibrational lines. Results. We find that L1489 IRS is well described by a central stellar mass of 1.3 ± 0.4 M_⊙ surrounded by a 0.10 M_⊙ flattened envelope with approximate scale height h ≈ 0.57R, inclined at 74°^+16°_-17°. The velocity field is strongly dominated by rotation, with the velocity vector making an angle of 15° ± 6° with the azimuthal direction. Reproducing low-excitation transitions requires that the emission and absorption by the starless core 1′ (8400 AU) east of L1489 IRS is included properly, implying that L1489 IRS is located partially behind this core. Conclusions. We speculate that L1489 IRS was originally formed closer to the center of this core, but has migrated to its current position over the past few times 10⁵ yr, consistent with their radial velocity difference of 0.4 kms^-1. This suggests that L1489 IRS' unusual appearance may be result of its migration, and that it would appear as a "normal" embedded protostar if it were still surrounded by an extended cloud core. Conversely, we hypothesize that the inner envelopes of embedded protostars resemble the rotating structure seen around L1489 IRS.