The 34-year-old also believes that the Baggies can challenge for a European qualification spot during the 2013-14 campaign.
"I think I will finish in England, I'm happy here," Anelka told the club's official website. "I also hope that it will be with this club.
"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 has now signed for six Premier League clubs during his career.