The Irons have chased Onana throughout the transfer window, but saw three bids rejected by the Ligue 1 outfit.
At the fourth time of asking, and with the fee reaching £40million, Lille eventually accepted the offer.
Despite reaching an agreement on the price tag, West Ham are still a long way from agreeing personal terms with the player, according to Sky Sports.
While Lille are reluctant to part ways with the Belgium international, they are conscious that a deal of such magnitude for Onana may not come around again. The 20-year-old arrived in Ligue 1 from Hamburger SV and made 43 appearances for the club across all competitions.
The player signed a five-year deal with Lille, meaning his contract expires in the summer of 2026.
Onana has Champions League football under his belt, having featured for the Mastiffs against Chelsea in the round-of-16 last season.
The youngster made his senior international debut back in June. Onana took part in a Nations League clash against the Netherlands after impressing manager Roberto Martinez.
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