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The 34-year-old former France international has been absent from the Midlands side following the death of his friend and agent Eric Manasse, with some reports suggesting Anelka was on the verge of quitting the game completely.
However, an Albion statement said: "Albion can confirm that Nicolas 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)."
Clarke made it clear after Tuesday's 3-0 win over Newport in the League Cup he was eager to find out what Anelka's plans were given it was not long before the transfer window closed.
"The situation has not really changed," Clarke said.
"But I'm conscious time is short in the remaining part of the transfer window so it's something I'll try to address tomorrow. We have to try to arrange a meeting as quickly as we can to try to get it sorted.
"I have to sit down and speak to Nicolas. That's the first thing. We have to get in touch with him or he has to get in touch with us and we have to see where he is, where he's at, how he feels, as quickly as possible. We have to have that chat.
"The furthest away he can be is London, because that's where he lives. I don't think he has a house in France. He's not there, as far as I know."
Anelka's much-travelled career has taken him to six countries and six Premier League clubs too.
He joined West Brom on a one-year deal in July but his only appearance for the Baggies to date came in a 1-0 defeat by Southampton in the opening game of the season.
