The striker, who only moved to France this month from Russian club Anzhi Makhachkala, had been expected to be loaned out to West Ham but Everton have moved in ahead of the Hammers to capture the 6' 8" striker.
Everton are looking to bring in another striker after selling Nikica Jelavic to Hull City.
The 23-year-old Traore signed a four-and-half year contract with Monaco at the start of the transfer window.
Traore scored 12 goals in 24 games last season after joining Anzhi from Kuban Krasnodar in June 2012.
The giant Traore will become the tallest ever outfielder to play in the Premier League when he appears for the Toffees. He would also equal in height the Premier League's tallest player – Manchester City keeper Costel Pantilimon.
Traore is the latest player to leave the struggling Russian club after billionaire owner Suleiman Kerimov cut spending amid frustration with their lack of success since his 2011 takeover.
Anzhi are bottom of Russia's top flight having sold Brazil playmaker Willian and Cameroon striker Samuel Eto'o to Chelsea, and Russia midfielder Oleg Shatov to Zenit St Petersburg.
Monaco, owned by Russian billionaire Dmitry Rybolovlev, have spent heavily to build a team challenging for the Ligue 1 title.
Promoted Monaco signed big names like striker Radamel Falcao from Atletico Madrid, plus his Colombia team-mate James Rodriguez and Portugal's Joao Moutinho from Porto before the season began.
Traore, who has scored four goals in seven internationals, was in the Ivory Coast squad that lost in last year's African Nations Cup quarter-finals to eventual winners Nigeria