"We consider it necessary and correct with the interests of the team as a guide," the KSI chairperson Vanda Sigurgeirsdottir said in a statement.
Iceland qualified for their first European Championship in 2016, beating England 2-1 in the last 16 before being knocked out in the quarter-finals by France.
They also qualified for the 2018 World Cup but earned only one point in the group stage with a draw against Argentina.
"Arnar has done many good things here at KSI and deserves praise for his work, which was often done in challenging situations," the KSI added.
Vidarsson, who earned more than 50 caps for Iceland during his playing career, was appointed head coach in December 2020.
Iceland beat Liechtenstein away 7-0 in Euro 2024 qualifying this week after losing their opening qualifier 3-0 to Bosnia and Herzegovina.
