Mourinho arrived in Milan last night at 10:45pm after a flight from Portugal and was met by Inter director Marco Branca at the Principe di Savoia.
Mourinho will be unveiled at a press conference this morning.
A statement on Inter's website said: "Internazionale announce the arrival of Jose Mourinho.
"The Portuguese coach has signed a three-year contract and will work alongside Rui Farias, Silvino and Andrei Villas Boas.
"The assistant coach will be Giuseppe Baresi."
Farias, Silvino and Boas were all part of Mourinho's backroom set-up at Chelsea, while Baresi is the head of the Italian outfit's academy.
The club added: "Thanking Roberto Mancini and his staff for the success obtained in four seasons as the leader of the team, all of Internazionale has the great pleasure to welcome Jose Mourinho and his coaches."