The 26-year-old confirmed via Twitter on Tuesday evening that he was heading out of Bordeaux and into St James' Park.
He has now arrived in England and made his way to Newcastle's training ground.
Should he sail through medical tests, Gouffran will then be clear to put pen to paper on a long-term contract.
His arrival will strengthen the French influence at St James' Park, with Alan Pardew having dipped into the Ligue 1 ranks on a regular basis of late.
Mapou Yanga-Mbiwa made a move from Montpellier on Tuesday and a deal has been put in place for Nancy's Massadio Haidara.
They will join the likes of Hatem Ben Arfa, Yohan Cabaye, Sylvain Marveaux and Mathieu Debuchy on Tyneside.