The 34-year-old former France international also has the option of a further 12 months and is hoping to see out his footballing days in the Black Country.
He told the club's official website, www.wba.co.uk: "I think I will finish in England, I'm happy here. I also hope that it will be with this club. I think this is the right club for me.
"I'm 34 years old now and I want to enjoy my football. I hope everything will be perfect.
"I hope we will be successful this year and hopefully we will reach Europe. We will try to do better than last season.
"That's why I'm here. When I spoke with the head coach, he said he wants to do better than last year. We will try our best to do that.
"We will also try to do the same in the cup competitions."
Anelka's relationship with Baggies boss Steve Clarke, who he also worked with at Chelsea, proved key in his decision to return to England from his short spell at Juventus.
He said: "I know the club and I know the head coach, which was very important for me.
"He knows how to use me on the pitch, which is important later on in your career.
"I know he likes to play football and that's why I signed here. He knows me and I know him. I also have friends in the changing room."
The sight of Anelka in an Albion shirt may come as something of a relief to the club's fans, who have previously seen him score five times in seven appearances against his new employers.
Anelka said with a smile: "I've always liked West Brom.
"I have a lot of good memories of playing against West Brom, and now I have to do my best to score for West Brom. When I was playing for Chelsea, it was always tough to beat Albion.
"The team plays good football and I know I will be able to play my game here. Hopefully I will be able to help the team win more games.
"I don't know which position I will play. As long as I'm playing and enjoying my football, I'm happy."