Traore had already obtained a work permit ahead of his switch to the English Premier League club earlier in the week, but the deal was briefly held up after Monaco striker Radamel Falcao was ruled out for several months with a knee injury.
Everton manager Roberto Martinez remained confident Traore would still be allowed to move to Goodison Park and the Toffees were finally able to clinch the deal for the 6ft 8in striker.
The 23-year-old, who had only joined Monaco from Russian club Anzhi Makhachkala earlier in the month, will replace Nikica Jelavic in the Everton squad after the Croatian joined Hull recently.
"The forward will require a visa before playing for the Toffees, a formality that is expected to be completed in the coming days."
Everton's move for Traore has not gone down well with West Ham manager Sam Allardyce, who came close to sealing a deal for the striker before Martinez stepped in.
Allardyce has been trying to strengthen his attacking options in the transfer market and was frustrated at missing out on Traore.
Asked if he is likely to make any signings before next week's match at Chelsea, Allardyce said: "I wouldn't have a clue at the minute.
"Every time I get a new signing somebody else takes him."