Mattiacci, formerly head of the Italian carmaker's North American operations, was named chief of Ferrari's competition division, including the Formula One team, on Monday after Stefano Domenicali took responsibility for the poor start to the season and resigned as team principal.
Mattiacci revealed on Friday ahead of the Chinese Grand Prix how fast things had moved between him being offered the job and accepting it.
"I received a call at 5.58 on Friday morning and chairman Montezemolo on the phone told me, 'this is my idea.'
"And I told (him) that April Fool's (day) was already far away, 15 days earlier," said Mattiacci, who lives in New York.
"But then after the second, third minutes of discussion, I understood it was serious and I understood that there was already a ticket ready to go from New York to Milan after three hours.
"And I arrived Saturday morning in Maranello at the Fiorano track."
Ferrari's decision to appoint Mattiacci to lead the sport's oldest and most successful team has been met with widespread scepticism.
Many have questioned whether the Italian, an outsider to the cut and thrust world of Formula One with practically no racing experience, will be able to turn the team's fortunes around.
"It is very motivating for me. And the fact that I need to prove that I am at the level of Ferrari, first, and the level of Formula One, so you have in front of you an extremely motivated person," Mattiacci said.
"I come with a lot of humility to understand and to work very hard.
"This is what I can commit to the team, to the drivers that are the best drivers in the world.
"They will have an extremely humble person that will listen and will fight 150 percent to be a facilitator and to utilise the best the talent that is within Ferrari."
Mattiacci also said that as part of getting up to speed with his new role, he had sat down with Domenicali to discuss what the job involves.
"Stefano is a person that I have the utmost respect for, first as a human being, second as a professional so it was natural for us to discuss the role," he said.
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- Stefano Domenicali