The France Under-21 international has found himself surplus to requirements at the Rossoneri and featured in just 15 games last season.
The 21-year-old is looking forward to the move back to his homeland which could be made permanent should Bordeaux decide to exercise an option in the deal.
Gourcuff told French newspaper L'Equipe: 'It is the ideal solution for me. The coming season is very important for the continuation of my career.
'Bordeaux is a regular and stable club. It is a one-year loan deal with an option to buy.'