The 26-year-old has joined for an undisclosed fee, agreeing a four-and-a-half year deal.
His arrival comes on the same day as Newcastle unveiled defender Mapou Yanga-Mbiwa who joined from Montpellier on Tuesday night.
Gouffran, a former France Under-21 international, scored 40 goals in 179 appearances for Bordeaux in a four-and-a-half year spell since signing from Caen.
He will now be charged with scoring the goals Newcastle need to climb away from the relegation battle at the foot of the Barclays Premier League.
Gouffran: "I am really proud to have joined this fantastic club.
"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."
Alan Pardew: "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."
Source: Newcastle United Mad