The club's official statement announcing Ausilio's exit carried a message from Marotta expressing gratitude on behalf of the entire organisation.
"I wish to thank Piero on behalf of the whole club, the ownership and every single employee of the great Inter family," Marotta said in the statement.
"Moments of joy, of victories, of intense work and great passion bind me to him."
Baccin, who has worked closely with the first team and the club's technical area, immediately steps into the newly created role of Chief Sport Officer.
Marotta framed the change as continuity rather than upheaval.
"Dario knows the club well and is ready today to take on this new role that the ownership and I have designed for him," he said. "It's an innovative choice, though one made in the spirit of managerial continuity.
"Dario has for many years been a fundamental part of the technical area and is the manager who worked on creating the Under-23 side in close connection with the first team, with a view to the progressive and sustainable development of the club."
Speaking separately to Sky Sport on the sidelines of Milan's Gran Gala del Calcio, Marotta elaborated on the decision to part ways with Ausilio after nearly three decades at the club.
"After 28 years spent, I'd say, doing well at Inter on Ausilio's part, we mutually arrived at this decision," Marotta said. "Our paths have separated in full respect of professionalism and friendship. We have great gratitude for him and we wish that the future can bring him the satisfaction he was able to find in a senior role at Inter."
On Baccin's promotion, Marotta pointed to a pattern the club has followed before.
"It's a point of pride to be able to draw on internal resources when changes happen," he said. "We did it with Chivu last year, we're doing it again this year with Baccin. We're entrusting this role to an executive with Inter in his DNA, who has been at the club for more than ten years. We're confident he can worthily replace his mentor, as Piero's own pupil."
Pressed on the underlying reasons behind Ausilio's sudden departure, Marotta declined to go into detail but insisted the split had been entirely amicable.
"It wouldn't be right to go into the specifics," he said. "I've spent the whole day with Piero, who has an excellent relationship with the ownership, with me and with everyone else at Inter. It seems normal to me that after such a long period someone might want to test themselves elsewhere or take a sabbatical.
"It all happened in a very conciliatory and respectful way, between people who hold each other in high esteem."