Correa has been reunited with Simone Inzaghi, joining the Nerazzurri on loan before making a permanent move to San Siro.
Lazio revealed Inter will pay an initial fee of €5million for the Argentina international, with a further €1m potentially due depending on performances.
Inter will then be obliged to spend another €25m to complete a permanent deal for Correa, who has agreed terms on a four-year contract with the Serie A champions.
The arrival of Correa is a boost for Inter following the departures of key men Romelu Lukaku and Achraf Hakimi to Chelsea and Paris Saint-Germain respectively.
Correa scored eight goals in 28 Serie A games last season, providing three assists and creating 29 chances under Inzaghi
Inter's new recruit could make his debut against Verona on Friday.