Andreolli left Inter for Roma as a 21-year-old in 2007 and has spent subsequent spells at Vicenza, Sassuolo and Chievo before opting to return to San Siro on a free transfer.
And the former Italy Under-21 centre-half is eager for the new season to get under way as Inter look to improve on last term's disappointing ninth-place finish.
He told a press conference: "For me it's a homecoming. I remember the day I left, I was really sad to be leaving Inter and it's great to be back after so many years.
"I have improved and I have a real sense of pride to be back here.
"I always wanted to come back and have worked hard for it."
Mazzarri was brought in by Inter this summer after guiding Napoli to second in Serie A last season.
The 51-year-old had an impressive record in Naples and has already made a good impression on Andreolli.
He added: "I have been struck by his will and determination.
"Also, I would like to emphasise the desire of the champions in the squad. They all have the desire to improve and are the leaders of the group."