The Russian star was one of the key targets for Chelsea owner and compatriot Roman Abramovich, and The Blues have snapped up the international midfielder for £3.4 million.
"After several days of discussions, Alexei Smertin has moved to Chelsea after three years of wonderful service to this club," Bordeaux announced on their official website.
"In three years with this club, Smertin contested 85 matches and always showed the same desire for victory, the same courage and the same conviction.
"The football club Le Girondins de Bordeaux would like to wish Alexei Smertin the best of luck."
Chelsea also confirmed the deal stating: "The signing has been completed of Russian international Alexei Smertin."
Chelsea are now expected to loan out the player, with Portsmouth the club most heavily linked.
The Blues are also expected to seal a deal for Hernan Crespo in the coming days - which would take Abramovich's spending to over £100 million on new players for club.
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