Mourinho on Monday became the 13th coach in the Moratti era at Inter, signing a three-year contract with the Serie A champions to replace Roberto Mancini, who was sacked last week.
Mourinho's predecessor was the most successful Inter coach in the 14 years Moratti has been president of the Nerazzurri, winning no fewer than seven titles in four years, including three consecutive Serie A titles.
But he was unable to provide the one trophy Moratti craves more than anything - the Champions League - and that will be the number one priority for Mourinho next season.
The rumour mill has already thrown up a number of names to help him clinch that prize for the second time after an unlikely success with Porto in 2004.
Unsurprisingly, many of Mourinho's closest allies at Chelsea, including Didier Drogba and Frank Lampard, have been placed at the top of the list, but Moratti admits the team which starts the defence of their Scudetto next season may look familiar.
"I have read lots of names but I have yet to speak with him (Mourinho) about the transfer market," revealed Moratti.
"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 as Mourinho adds his own hallmark to the already richly-assembled squad.
And that may mean there is no room for Argentinian striker Hernan Crespo, who played very little under Mourinho during his Chelsea days.
Nevertheless, Crespo is not apprehensive about meeting Mourinho again.
"I have no problems with him and will be available to play like a professional should always be," he said.
"I do not fear a competition for places and, in a big club, there will always be lots of big players, but that is part of the game.
"There was room for everybody at Chelsea. Mourinho acts correctly and explains the situation to you always and I respect him."
Mourinho will set out his plans on Tuesday when he is presented to the media at Inter's training facilities, filling the shoes of a man who provided so much joy to the success-starved Nerazzurri followers recently.
And while Mourinho is now the future of Inter, many words of thanks have been reserved for Mancini who, according to Paolillo, "is an equally great coach and a true professional.
"Such is life: in every company, the best of bosses are often replaced by equally good professionals," he added on Sky television.
Whether the gamble pays off this time will be revealed by May 27 next year, when Mourinho's Inter aim to leave the field triumphant at Rome's Stadio Olimpico, having cracked the Champions League code at the 13th time of asking.
It is an expensive gamble with the 45-year-old reportedly earning nine million euros a year, not to mention the huge payout for his predecessor, who was contracted to the club until 2012.
Mancini's departure was a protracted affair, with reports last week suggesting there had been a breakdown in communication between the coach and president Massimo Moratti.
Mancini's agent claimed after Tuesday's 25-minute meeting between the pair that his client had left the club and would be replaced by Mourinho.
The Italian's dismissal was confirmed by the club on Thursday, just hours after Inter had threatened legal action because of reports they claimed did not "correspond to the truth of the facts".
Inter cited Mancini's announcement in the wake of their Champions League defeat to Liverpool on March 11 that he would step down at the end of the season had been a crucial factor.
Mancini reversed his decision 24 hours later and went on to lead Inter to their third straight Serie A title, but after much speculation, his departure was confirmed on Thursday evening.
Mourinho has long been linked with the post at the San Siro.
He was appointed as manager of Chelsea back in 2004 after leading Porto to the Champions League title.
He led Chelsea to back-to-back Premier League titles, but could not bring the Champions League trophy to Stamford Bridge in just over three years in charge at the London club.
He left Chelsea last September by mutual consent and has been linked with a host of top job jobs since.
Mourinho will have Giuseppe Baresi, who has been running Inter's youth academy, as his assistant - as well as a team of coaches including Rui Farias, Silvino and Andrei Villas Boas.