The announcement comes the day after Inter announced that coach Antonio Conte will leave the post a year before the contract expires, following a joint decision.
For Simone Inzaghi, at the same time, a 22-year history with Lazio is over.
"There are many emotions when I now tell you that my wonderful adventure with Lazio ends on June 30," Inzaghi told the news agency Ansa, reports Reuters.
Three cup titles
The now 45-year-old Inzaghi has been in the Roma club since 1999, when he came there as a player.
In 2010, he put his shoes on the shelf and first coached the youth team before he became head coach of the A-team in 2016.
Since then, he has led Lazio to a victory in the Italian Cup and two titles in the domestic Super Cup.
Last season, he led the team to the quarterfinals of the Champions League.
- I want to thank the club, the chairman, the players and the fans who have joined me during these wonderful 22 years.
We fought and won together, says Inzaghi.
"Never showed up"
But President Claudio Lotito is not as cheerful.
Sky Italia states that the club management on Wednesday agreed with Inzaghi on a contract extension, before Inter should have got him on other thoughts.
The Milan club is expected to present Inzaghi as the new coach on Friday.
- I had already signed the contract, but he never showed up to do the same, Lotito says to football-italia.net.
- It was a disappointment on a personal level. He changed from last night to this morning. He called, said he had slept on the matter and decided to leave. We sat together for seven hours yesterday, we reached an agreement and even shook hands on it.