The 27-year-old left Championship side West Bromwich Albion after his three-year contract expired this summer.
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Maja now returns to France, having previously enjoyed two spells with Bordeaux between 2019 and 2021 and again from 2022 to 2023.
He penned a one-year contract with Le Havre, including an option for a further season, and will wear the No. 9 shirt.
He is expected to provide experience and attacking depth as the club battle to remain in Ligue 1 beyond May 2027.
His arrival follows the departure of Issa Soumare, who joined Rennes as a free agent.