The 26-year-old has spent four and a half seasons with his current club but is set to join Newcastle's battle to avoid relegation from the Barclays Premier League and the growing French contingent at St James' Park.
He wrote on Twitter tonight: "Big thanks to everyone who has supported me through the good times and bad times. I thank the leadership of the club and the staff for helping me grow.
"I need a new challenge and therefore I hope that you respect my choice. I will follow all the results of the Girondins (Bordeaux).
"Tomorrow I will be a new player of Newcastle and I am proud. Thanks to everyone....kisses."
Gouffran was left out of Bordeaux's squad for tomorrow's Coupe de France match against Moulins. He was listed as 'absent' rather than named on the injured or suspended lists by Bordeaux.
His Bordeaux contract is due to expire in the summer and the question of whether he would renew has lingered for months, with his declaration that Newcastle have attracted him to England apparently bringing the saga to an end.
Newcastle boss Alan Pardew is also expected to sign defenders Mapou Yanga-Mbiwa and Massadio Haidara from French clubs within the next 48 hours while hopes are also high that the Magpies will win the race to sign Moussa Sissoko from Toulouse.
Montpellier confirmed the departure of Yanga-Mbiwa pending a medical on their official website, with a fee believed to be in the region of £7million agreed for the French international.
A statement from Ligue 1 strugglers Nancy confirmed that 20-year-old full-back Haidara is also set to join the Magpies subject to a medical following an agreement between the clubs.
Their statement said: "After 46 games and two and a half years in the Nancy shirt, Massadio Haidara is leaving for Newcastle United, currently 16th in the Premier League.
"The two clubs have reached an agreement and will finalise the transfer on Tuesday."
The deals will come as a great relief for Pardew, who was put under more pressure by Saturday's shock 2-1 home defeat to Reading, which left Newcastle languishing just two points above the relegation zone.
The news of deals in the offing came hot on the heels of frustration in the transfer market for Pardew, who lost out in the bid to sign striker Loic Remy from Marseille. Another French defender, Mathieu Debuchy, remains his only January signing to date.
Yanga-Mbiwa told Montpellier's official website he is relishing his move and said: "This (England) is a country where everybody loves football and I really want to experience this culture. It is one of the things you want to discover as a player.
"I feel I have given everything to the maximum while at Montpellier. They have been like my second family and have given me everything. There were hard times and good times but there is a very strong bond that unites us."
Newcastle's chase for Sissoko looked set to pay off when the player was left out of the squad for Toulouse's scheduled French Cup clash with Paris St Germain tomorrow night.