The 20-year-old moves to the San Siro after completing a five-year contract.
Laxalt played in all seven of Uruguay's matches at the recent Under-20 World Cup in Turkey, where his country finished as runners-up to France following a penalty shoot-out defeat in the final.
His arrival is another sign of Inter's rebuilding work following a disappointing Serie A campaign in 2012-13.
Inter finished ninth under previous coach Andrea Stramaccioni, their worst performance in Italy's top flight since 1994.
Stramaccioni's replacement Walter Mazzarri has reinforced his squad with Mauro Icardi and Ishak Belfodil from Sampdoria and Parma respectively prior to Laxalt's arrival.