The 26 year old will boost the striking options Alan Pardew has available to him.
“Throughout the last few years I have enjoyed every moment of my time at Bordeaux but all good things must come to an end and it was time for a new challenge,” said Gouffran.
“The challenge of playing for one of the most famous teams in England, with all of its history and its famous support, is very exciting.”
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.