The 25-year-old French midfielder will officially join Mauricio Pochettino’s side on 1 July when his contract at RB Leipzig expires.
The Blues’ co-sporting directors said: "Christopher has proved himself one of the standout attacking players in European football over the past two seasons and will add quality, creativity and versatility to our squad.
"He has demonstrated his ability at the highest level with RB Leipzig and France and we look forward to him joining up with his new team-mates ahead of the new season."