The 30-year-old is reported to have penned a four-year deal with Los Blancos, with his former Serie A side set to receive 20 million Euros for the move.
According to journalist Fabrizio Romano, the Dutch international had completed his medical last week and is set to be an important part of Madrid's squad campaign after a disappointing 2025/26 campaign.
He is set to join the Spanish giants after the 2026 FIFA World Cup tournament with the Netherlands, whom he has 72 caps for, scoring 11 goals.
Dumfries won eight domestic trophies with the Nerazzurri including the league and cup double in the recent 2025/26 season.
Madrid have already secured Ibrahima Konate from Liverpool on a free transfer and are bidding for rival Atletico Madrid striker Julian Alvarez, with their rivals refusing to entertain the sale of the Argentine.