The Ivorian striker has joined for an undisclosed fee believed to be in the region of €12m and has signed a four-and-a-half year deal with the Ligue 1 side.
Monaco however are believed to be open to the idea of sending Traore to West Ham for the remainder of the Premier League season.
There is some speculation that Traore has been bought as a long-term replacement for Falcao who could leave Monaco in the summer.
At 6' 8" Traore would become the tallest ever outfielder to play in the Premier League should he appear for the Hammers. He would also equal in height the Premier League's tallest player – Manchester City keeper Costel Pantilimon.
Traore scored 12 goals in 24 Russian League games last season and has also netted five times in 12 Europa League games.
He has been capped seven times for the Ivory Coast – scoring four times.