We present a study of rotation across 30 square degrees of the Orion Star-forming Complex, following a ∼200 d photometric monitoring campaign by the Next Generation Transit Survey (NGTS). From 5749 light curves of Orion members, we report periodic signatures for 2268 objects and analyse rotation period distributions as a function of colour for 1789 stars with spectral types F0–M5. We select candidate members of Orion using Gaia data and assign our targets to kinematic sub-groups. We correct for interstellar extinction on a star-by-star basis and determine stellar and cluster ages using magnetic and non-magnetic stellar evolutionary models. Rotation periods generally lie in the range 1–10 d, with only 1.5 per cent of classical T Tauri stars or Class I/II young stellar objects rotating with periods shorter than 1.8 d, compared with 14 per cent of weak-line T Tauri stars or Class III objects. In period–colour space, the rotation period distribution moves towards shorter periods among low-mass (>M2) stars of age 3–6 Myr, compared with those at 1–3 Myr, with no periods longer than 10 d for stars later than M3.5. This could reflect a mass-dependence for the dispersal of circumstellar discs. Finally, we suggest that the turnover (from increasing to decreasing periods) in the period–colour distributions may occur at lower mass for the older-aged population: ∼K5 spectral type at 1–3 Myr shifting to ∼M1 at 3–6 Myr.