The Toffees have the option to buy the 27-year-old on a permanent deal at the end of the season.
Sidibe won the Ligue 1 title with Monaco in the 2016-17 season and was part of the France squad that lifted the World Cup in Russia last year.
He has scored six goals in 114 appearances for Monaco since joining from Lille in 2016.
The defender will provide competition at right-back for Ireland international Seamus Coleman.
Everton manager Marco Silva said: “It is important to have different options in each position and with Djibril and Seamus, 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.”
Sidibe is Everton’s sixth signing of the summer after goalkeeper Jonas Lossl, midfielders Andre Gomes, Fabian Delph and Jean-Philippe Gbamin, and striker Moise Kean.
The Merseyside club remain interested in signing Crystal Palace winger Wilfried Zaha before Thursday’s transfer deadline.
Find all the latest football transfers on our dedicated page.