The 34-year-old former France international has been away from the club following the death of his close friend and agent Eric Manasse.
Anelka even reportedly talked about quitting football altogether, but Albion this evening confirmed his intention to play on.
The club revealed the striker is to resume first-team training tomorrow and will be available for selection for Sunday's game against Swansea.
"Albion can confirm that Nicolas Anelka will resume first-team training tomorrow and be available for selection for Sunday's game against Swansea," a statement on the club's official website, www.wba.co.uk, said.
"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."
Anelka's return will be a huge relief to Clarke, who was facing up to the prospect of losing a player he had signed just weeks ago.
The West Brom boss had on Tuesday night said he was eager to sit down with the Frenchman to seek clarification on his future.
"The situation has not really changed," Clarke said after watching his side ease past Newport and into the Capital One Cup third round with a 3-0 win.
"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 long and varied career has taken him to six countries, with spells at clubs varying from Real Madrid and Juventus to Bolton and Shanghai Shenhua.
West Brom became the sixth Premier League club of his career when he joined on a one-year deal in July.
Anelka's only appearance for the Baggies to date came in a 1-0 defeat to Southampton in the opening game of the season.