The 22-year-old joins The Navy Blue and Whites on a four-year deal after rejecting a contract extension at the club.
He made 30 league appearances for Nantes last season, starting 22 of those games.
"Enock Kwateng has today signed for four seasons with FC Girondins de Bordeaux," Kwateng's new club announced via their official website.
"At the end of his contract with Nantes, the right-back has signed a contract [with Bordeaux which runs] until June 2023.
"He will join the professional group as soon as training resumes.
"The club is delighted to be able to count in its ranks a young talented player like him."
Born to Ghanaian parents in France, Kwateng has represented the European nation at various youth levels.
He has indicated his readiness to switch international allegiance to play for Ghana at senior level.