The experienced former French international has been given a 12-month contract by the Baggies, who have the option of adding a further year to the deal next summer.
And the much-travelled 34-year-old, who has already played in the English top flight for Arsenal, Liverpool, Manchester City, Bolton and Chelsea, is pleased about his latest move.
"I think I will finish in England, I'm happy here," he said. "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 want to enjoy my football.
"I hope we will be successful this year and hopefully we will reach Europe. When I spoke with the head coach, he said he wants to do better than last year."
Anelka is familiar with Steve Clarke from his time at Chelsea and added: "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. I also have friends in the changing room."
Anelka arrived at West Brom for his medical on Thursday morning and is impressed with what he has seen of the club.
"I know it's a big club and a family club," he said.
"The Hawthorns has a good atmosphere, like many of the Premier League stadiums.
"The facilities at the training ground are also amazing. I'm sure I will enjoy my training and hopefully that will extend to the stadium."