The Sun says the French striker, 34, agreed a £5million, two-year Baggies deal which will pocket him £50,000 a week at The Hawthorns.
It is nowhere near the £20m he got from Shanghai Shenhua in December 2011. But it still beats Baggies' current highest-paid stars - Swede Jonas Olsson and Peter Odemwingie - who are both on £40k a week.
Albion boss Steve Clarke said: "This is a great boost. The more quality stars you can bring in the better and no one can question Nicolas' quality.
"I worked with him at Chelsea.
"He's got a great work ethic and if you add that to the obvious talent he's got I think he can be a top signing."