The reported Tottenham Hotspur target, who scored 24 league goals last season as surprise packages Genoa bagged a Europa League spot, has penned a four-year deal with the Italian champions.
An Inter statement gave no details of the fee.
Genoa are also in the process of signing Inter's Argentine forward Hernan Crespo and Atalanta striker Sergio Floccari.
To make room for the new players which Mourinho hopes will give Inter more edge in the Champions League, forward Julio Cruz is leaving with Fiorentina expressing an interest.
Media reports say French midfielder Patrick Vieira wants to return to France.
NEWS: Mourinho confirms move for Milito
NEWS: Tottenham target holds talks with Inter
BLOG: Milito the man to help Ibrahimovic silence San Siro boo-boys
