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."
Mourinho has been heavily linked with the role at Inter and has reportedly been taking Italian lessons ahead of any possible appointment.
Inter appear to have drafted in Mourinho to help improve their success in Europe.
Despite their domination on the domestic front, they have struggled in the Champions League and were beaten at the last 16 stage by Liverpool.
"Serie A is feeling a little tender right now and perhaps not enjoying its status like before so having Mourinho joining is a very positive thing," said Italian football expert James Richardson.
While at Porto, Mourinho won the Uefa Cup in 2003 and the Champions League in 2004.
He also led Chelsea to the Premier League title in 2005 and 2006, while the Stamford Bridge side were beaten by Liverpool twice in the semi-finals of the Champions League in 2005 and 2007.
I would like to change very little of this squad which has won so much
Inter president Massimo Moratti
Mourinho is expected to have plenty of money to strengthen the side and he has reportedly maintained contact with some of his former Chelsea charges.
He has already been linked with Frank Lampard and Didier Drogba and no-one would be too surprised if one, or both, joined Mourinho at Inter before the new season begins.
Inter president Massimo Moratti said: "I have read lots of names but I have yet to speak with him (Mourinho) about the transfer market.
"I would like to change very little of this squad which has won so much."
General manager Ernesto Paolillo added that there would be "few, but good players" arriving this summer.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.