The former France international had been away from the club following the death of his close friend and agent Eric Manasse and has even reportedly talked about quitting football altogether.
"Albion can confirm that Nicolas Anelka will resume first-team training and be available for selection for Sunday’s game against Swansea," the club said in a statement.
"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, he will rejoin his team-mates."
Anelka wrote on his Facebook page last Thursday: "I've just learned with deep sadness the death of mister Eric Manasse. I can't find the words to express my huge grief and I wanted to pay condolences to the Manasse family after this tragic death."
The 34-year-old Anelka joined West Brom, his sixth Premier League club, on a free transfer last month and featured in their opening game defeat at the hands of Southampton on Saturday.
He moved to Chinese club Shanghai Shenhua from Chelsea in January 2012 but did not settle and went out on loan at Juventus.