A statement on the club website said the 34-year-old had signed a one-year contract with a further year's option in the club's favour.
Anelka, who has played for Arsenal, Liverpool, Manchester City, Bolton and Chelsea, was a free agent after ending his loan spell with Juventus at the end of last season.
"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," 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 got a great work ethic, looks after himself and is a consummate professional. His experience with some of the top clubs in England and Europe will stand the group in good stead."
