West Brom manager Steve Clarke admitted last week that the 34-year-old Anelka had told him he was considering retirement.
"Albion can confirm that Nicolas Anelka will resume first-team training tomorrow and be available for selection for Sunday's game against Swansea," the club said in statement on their website.
Anelka joined West Brom, his sixth Premier League club, on a free transfer last month and played in their opening defeat at home to Southampton.
West Brom have one point from two games.
(Writing by Gregory Blachier in Paris; Editing by Ed Osmond)
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