Following the expiry of Dani Carvajal's contract, Alexander-Arnold had been the only recognised senior right-back in the squad. Dumfries now arrives to provide competition and depth in the position.
Dumfries leaves Inter after five productive seasons in which he established himself as one of Europe's most consistent wing-backs. He made 207 appearances for the Italian club, scoring 27 goals and providing 28 assists while helping the Nerazzurri win two Serie A titles.
Although his final campaign was disrupted by ankle surgery, the 30-year-old still featured 28 times and scored five goals. His arrival gives Madrid another experienced option on the right side of defence.