Mazzarri confirmed last weekend that he would be leaving Napoli and reports quickly suggested he would replace Stramaccioni at Inter.
Stramaccioni's 14-month tenure at the San Siro has come to an end after a disastrous season by Inter's standards, which has seen the club fail to qualify for Europe next season.
A run of eight defeats from 11 games, and a total of 16 in a dismal campaign, left Inter in ninth place in Serie A and with no European football for the first time since the 2000/01 season.
Nerazzurri president Massimo Moratti had refused to divulge any details from a series of meetings held this week at Inter's headquarters in central Milan when he was quizzed by reporters earlier on Friday.
However, Inter have now released a statement to confirm that Stramaccioni has been dismissed and replaced by Mazzarri.
Explaining the decision to sack Stramaccioni and appoint Mazzarri, Moratti told the Italian media: "All sackings are not good, but it's a change due to the fact that this next season will be a difficult year and I thought there was the need of a coach with Mazzarri's experience.
"Anyway, there is still regard for the talent and the possibilities of Stramaccioni, and I'm convinced he will become one of the best Italian coaches.
"Mazzarri is a choice made with attention. Now, we will see what we will do during the transfer window.
"We have a coach with whom we will talk about this and then we will see what will happen."
The 51-year-old led Napoli to the runners-up spot in Serie A this season, but had decided to take on a fresh challenge following four years with the club.