Dier will sign a contract at Monaco until 2027, with an option for an unspecified extension.
The 31-year-old Englishman's contract with Bayern Munich expires this summer. Dier first came on loan from Tottenham Hotspur in January 2024 and was eventually signed permanently.
He has played an important role in the German record champions' defence this season due to a number of injuries.
Dier has made 25 appearances in all competitions so far, scoring two goals and setting up another.
No personnel shortage
This will not create a hole in Munich's central defence. Dayot Upamecano and Hiroki Ito are expected to have recovered from their injuries for the new season, as is youngster Tarek Buchmann.
Josip Stanisic and Min-jae Kim are also still available, should the South Korean not be sold in the summer.