The highly-rated 23-year-old arrives at Ewood Park on loan and his French employers have emphasised there is no option to buy.
Bordeaux paid Nice 3.5million euros for Modeste in August 2010, and although he has failed to make a huge impact at the Parc Lescure they still see a future for him at the club.
Blackburn have now moved to finalise a deal and they are hoping the striker will receive international clearance in time to feature in Saturday's clash against Everton.
The Cannes-born forward scored three goals for Bordeaux in 15 Ligue 1 appearances this season. His last goal for Les Girondins was scored in a 2-0 win over Caen in November.
He is Rovers boss Steve Kean's first significant acquisition of the January transfer window.
Kean admits that Modeste has a lot to prove after the former France Under-21 striker's failure to live up to expectations at Bordeaux.
Modeste had attracted interest from Arsenal when at Nice after scoring six goals in 15 appearances for France Under-21s but his career then failed to take off.
Kean said: "He's got a lot to prove as he went to Bordeaux for a big fee but I think he could be a real addition to our squad.
"He's not too young but he's not in the twilight of his career either, and if you look at his attributes as a player he's got something we don't have.
"He likes to play on the shoulder of the defender, to run in behind, he can stretch the game and technically he's good.
"He would certainly complement the other strikers we have and we hope it will be an exciting loan period initially and that's something we could maybe continue further on."
Meanwhile, Scott Dann is back in the squad to travel to Everton after a groin injury.
