The former France international was granted compassionate leave to miss last Saturday's draw at Everton, but is now back in contention for this weekend's home clash with Swansea City.
Anelka moved to The Hawthorns in July and enjoyed a prolific pre-season, but failed to find the net on his debut against Southampton on the opening day of the Premier League season.
Head coach Steve Clarke had admitted the 34-year-old was considering quitting football, but he has now gone back on any such thoughts.
A club statement read: "Albion can confirm that Nicola Anelka will resume first-team training tomorrow and be available for selection for Sunday’s game against Swansea.
"The striker was excused from club duty for the fixtures against Everton and Newport on compassionate grounds and, having met with head coach Steve Clarke today, he will rejoin his team-mates tomorrow (Thursday)."
West Brom found form in midweek at home to Newport County in the League Cup, as young striker Saido Berahino scored a hat-trick to seal a 3-0 win over the League Two newcomers.
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