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Crystallization of the lunar magma ocean yielded a chemically unique liquid residuum named KREEP. This component is expressed as a large patch on the near side of the Moon and a possible smaller patch in the northwest portion of the Moon’s South Pole-Aitken basin on the far side. Thermal models estimate that the crystallization of the lunar magma ocean (LMO) could have spanned from 10 and 200 My, while studies of radioactive decay systems have yielded inconsistent ages for the completion of LMO crystallization covering over 160 My. Here, we show that the Moon achieved >99% crystallization at 4,429 ± 76 Ma, indicating a lunar formation age of ~4,450 Ma or possibly older. Using the¹⁷⁶Lu–¹⁷⁶Hf decay system (t_1/2= 37 Gy), we found that the initial¹⁷⁶Hf/¹⁷⁷Hf ratios of lunar zircons with varied U–Pb ages are consistent with their crystallization from a KREEP-rich reservoir with a consistently low¹⁷⁶Lu/¹⁷⁷Hf ratio of 0.0167 that emerged ~140 My after solar system formation. The previously proposed younger model age of ~4.33 Ga for the source of mare basalts (240 My after solar system formation) might reflect the timing of a large impact. Our results demonstrate that lunar magma ocean crystallization took place while the Moon was still battered by planetary embryos and planetesimals leftover from the main stage of planetary accretion. The study of Lu–Hf model ages for samples brought back from the South Pole-Aitken basin will help to assess the lateral continuity of KREEP and further understand its significance in the early history of the Moon.