Gouffran arrived on Tyneside earlier on Wednesday to undergo a medical and he has now put the finishing touches to his move to Alan Pardew's side.
The forward was due to be out of contract at Bordeaux at the end of the season and is understood to have cost Newcastle a fee in the region of £1.4million.
"I am really proud to have joined this fantastic club," Gouffran told Newcastle's official website.
"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.
"And 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."
Newcastle boss Pardew added: "Yoan comes to the club with a great pedigree and, like the other signings we have made this month, is a player who will add considerable strength to our squad.
"I liked the look of him when we played Bordeaux at St James' Park earlier this season; pacy, direct and intelligent and those are qualities I like in a footballer.
"I am sure he will quickly adapt to the rigours and intensity of the Premier League and play an important role for us for the remainder of the season."
Gouffran becomes the third arrival at St James' Park from Ligue 1 so far this month after defensive duo Mathieu Debuchy and Mapou Yanga-Mbiwa linked up with the Premier League strugglers.
Pardew is also hoping to tie up the signing of Nancy full-back Massadio Haidara, while Toulouse midfielder Moussa Sissoko has been strongly linked with a move to the North East.