Mourinho has signed a three-year deal with the Italian side in his first job since he and Chelsea parted company by mutual consent in September 2007.
The 45-year-old succeeds Roberto Mancini, who was sacked after leading the club to a third consecutive Serie A title last season.
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.