Our understanding of geomagnetic field intensity prior to the era of direct instrumental measurements relies on paleointensity analysis of rocks and archaeological materials that serve as magnetic recorders. Only in rare cases absolute paleointensity datasets are continuous over millennial timescales, in sub-centennial resolution, and directly dated using radiocarbon. As a result, fundamental properties of the geomagnetic field, such as its maximal intensity and change rate have remained a subject of lively discussion. Here, we place firm constraints on these two quantities using Bayesian modeling of well-dated archaeomagnetic intensity data from the Levant and Upper Mesopotamia. We report new data from 23 groups of pottery collected from 18 consecutive radiocarbon-dated archaeological strata from Tel Megiddo, Israel. In the Near East, the period of 1700–550 BCE is represented by 84 groups of archaeological artifacts, 55 of which were dated using radiocarbon or a direct link to clear historically-dated events, providing unprecedented sub-century resolution. Moreover, stratigraphic relationships between samples collected from multi-layered sites enable further refinement of the data ages. The Bayesian curve shows four geomagnetic spikes between 1050 and 600 BCE, with virtual axial dipole moment (VADM) reaching values of 155–162 ZAm2 – much higher than any prediction from geomagnetic field models. Rates of change associated with the four spikes are ~0.35–0.55 μT/year (~0.7–1.1 ZAm2/year), at least twice the maximum rate inferred from direct observations spanning the past 190 years. The increase from 1750 BCE to 1030 BCE (73 to 161 ZAm2) depicts the Holocene’s largest change in field intensity.