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Using Faraday rotation measures (RM) from the NRAO VLA Sky Survey catalogue we derive new, statistically robust, upper limits on the strength of extragalactic magnetic fields. We simulate the extragalactic magnetic field contribution to the RMs for a given field strength and correlation length, by assuming that the electron density follows the distribution of Lyman-α clouds. Based on the observation that RMs from distant radio sources do not exhibit any trend with redshift, while the extragalactic contribution instead grows with distance, we constrain fields with Jeans' length coherence length to be below 1.7 nG at the 2σ level, and fields coherent across the entire observable Universe below 0.65 nG. These limits are applicable to magnetic fields of both primordial and astrophysical origins.