The two clubs have agreed an undisclosed fee for the 27-year-old, who will complete his switch to the Ukraine after undergoing a medical.
"Girondins de Bordeaux and Dynamo Kiev have reached agreement for the transfer of Benoit Tremoulinas to the Ukrainian capital," read a statement on Bordeaux's official website.
"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 been capped twice by France at senior international level.