Anelka was a free agent after leaving Italian champions Juventus at the end of last season.
The French striker has signed a one-year contract, with a further year’s option for West Brom.
“We are missing a bit of firepower from last year – we’re trying to put that right – and to kick off with the signing of Nicolas at the start of the summer is a great boost for everyone at the club,” West Brom boss Steve Clarke said.
“The sole focus at the club is trying to build on what we did last season.
“The more quality players you can bring to the club the better – and no-one can question Nicolas’ quality.
“He’s a player I have worked with before as I was at Chelsea when they signed him.
“He’s got a great work ethic, looks after himself and is a consummate professional.
“If you add that to the obvious talent he’s got I think he can prove to be a really top signing for the club.
“His experience with some of the top clubs in England and Europe will stand the group in good stead.
“Hopefully he will be able to inspire the other players to even greater heights than we managed to achieve last year.”
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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.