The 27-year-old has been with his hometown club since joining their youth academy in 1994, though he did not make a first-team appearance until 2007.
The French side said on their official website: "Girondins de Bordeaux and Dynamo Kiev have reached agreement for the transfer of Benedict Tremoulinas to the Ukrainian capital.
"This transfer is not official yet. It will be when all the paperwork has been signed by the two clubs. Benedict must also pass the medical examination in Kiev.
"The club will keep fans informed if a formalisation of this transfer takes place in the coming days."
Tremoulinas has earned plaudits for his Ligue 1 performances in recent seasons and has made 200 career appearances for the club, providing 34 assists in the process.