"With this new agreement, the coach will lead the Nerazzurri until 2026," the club said in a statement.
Inzaghi took over in 2021 on a two-year deal following the departure of Antonio Conte, and extended his contract last September until 2025.
Inter finished 19 points ahead of AC Milan at the Serie A summit to seal a 20th league title with five games left following a 2-1 victory over their city rivals in April.
In three seasons the former Lazio coach also led the club to three Italian Supercups, two Italian Cups and the final of the Champions League in 2023.
While Inter went out in the round of 16 in both the Champions League and Italian Cup last season, they dominated Serie A with 29 wins, seven draws and just two defeats.
Inter changed ownership in May with US fund Oaktree taking over from Chinese group Suning, which was unable to repay a debt worth hundreds of millions of dollars.
