Basile Ader, a lawyer for the ailing 80-year-old president, told a Paris court Bouteflika's "magnanimous" decision came after a recent apology from the paper.
Le Monde's lawyer Christophe Bigot praised Bouteflika's "welcome" gesture.
At issue was an April 6, 2016, article by Le Monde titled "The hidden money of heads of state" that included a photo of Bouteflika among those of leaders implicated in the so-called Panama Papers, a trove of leaked documents that revealed murky offshore financial dealings involving shell companies designed to help the world's rich and powerful evade taxes.
That did not satisfy the Algerian authorities.
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During a visit to Algeria just days later by then French prime minister Manuel Valls, the paper's reporters were denied visas to travel to the former French colony.
Algeria's then prime minister Abdelmalek Sellal said the decision was taken because a "respected and respectable newspaper has gratuitously hurt (Bouteflika's) honour and prestige".
The names of dozens of family members and associates of prime ministers, presidents and kings around the world appeared in the Panama Papers.