Sidibe heads to Goodison Park on a one-year loan deal for a reported €2.5 million (£2.3m/$2.8m) loan fee with a €14m (£12.9m/$15.7m) option to buy in the summer.
The full-back is Everton's sixth signing of the summer after Moise Kean, Andre Gomes, Fabian Delph, Jonas Lossl, and Jean-Philippe Gbamin.
“I was very happy to hear a historic and big club like Everton was thinking of signing me," Sidibe said in a statement
“It was very easy for me. I did not have to reflect for too long before making my decision to come here.
“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.”
He made 47 total appearances for the club that season as Monaco lifted the Ligue 1 title for the first time in 17 years.
In total, he has earned 18 caps for France, scoring one goal at the international level.
“Djibril has fantastic experience, winning titles and playing many matches in a competitive league. He is a World Cup winner and he has the hunger to achieve much more in his career," said Everton boss Marco Silva.
“It is important to have different options in each position and with Djibril and Seamus [Coleman] we now have two high-quality right-backs.
“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.”
Everton open their Premier League campaign on Saturday against Crystal Palace.