“The decision to continue this journey together is the result of shared planning, strengthens the bond between the two parties and confirms the unity of intent needed to achieve our sporting objectives,” the team said in a statement.
Inzaghi, who played as a striker for 11 years with Lazio and won the club’s last Serie A title in 2000, took over as coach in 2016.
The 43-year-old won his first major trophy as a coach in this year’s Coppa Italia and had been linked to the vacant coaching positions at champions Juventus and AC Milan.
Lazio finished eighth in Serie A this season but qualified for the Europa League as Coppa Italia winners.