Sidibe, 27, helped Monaco win the Ligue 1 title in 2017 and was a member of the France squad who won last year's World Cup.
"It is important to have different options in each position and with Djibril and Seamus (Coleman), we now have two high-quality right backs," Everton manager Marco Silva said.
"Djibril has also shown to me he has a real desire to play for Everton and be part of the big things we are trying to create."
Sidibe, who has played 18 times for his country, said it was an easy decision to make.
"Everton are recruiting with the intent to win trophies and play on the biggest stage. I am 100 per cent motivated and ready to help the club achieve its goals and to achieve my own individual goals," Sidibe told Everton TV.
The defender arrives as Everton’s sixth summer signing, following goalkeeper Jonas Lossl, midfielders Andre Gomes, Fabian Delph and Jean-Philippe Gbamin, and striker Moise Kean.
But the Toffees remain active in the transfer window heading into deadline day as they retain interest in Crystal Palace winger Wilfried Zaha, who on Wednesday handed in a transfer request to try and force through a late move away from Selhurst Park.
Everton have faced competition from Arsenal for the 26-year-old Ivory Coast international, but retain hope of agreeing a deal to sign the former Manchester United player before the 5pm deadline.
The Merseyside club also saw a £30m offer for Arsenal’s Alex Iwobi rejected on Wednesday as a Plan B option for Zaha, while United defender Chris Smalling rejected a potential loan move to Goodison Park.
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