Anelka, 34, was a free agent after leaving Juventus in the summer. Clarke confirmed that the former France international had turned down more lucrative offers to return to England.
The Baggies' head coach said: "Nicolas was available and he wanted to come back and play in England.
"He still felt that he had enough in his body to produce in the Premier League - and luckily for him, I agreed.
"He's a player I know well from my spell at Chelsea.
"He will bring good quality to the group. I hope he will bring the rest of the players along and lift them to a higher level."
For the big stories and the banter follow us on Twitter: @tribalfootball