Inzaghi left Inter just days after their Champions League final defeat to PSG, though there's been claims he was speaking with Al-Hilal before the Munich clash.
"If it's the price to pay for four years at Inter, I'm happy to do it," said Inzaghi. "I received much more than I gave: from the fans, the directors, the players. I know I will miss everything, even the most unfair criticism.
"But I gave everything and I believe that, for the good of Inter, parting ways was the right choice, even if it was painful for everyone.
"After years at Inter, I needed to get out of my comfort zone. I wanted to change my mentality, my style of play and face new challenges. There was no other club I wanted to coach: I chose Al-Hilal."
Inzaghi will lead Al-Hilal for the first time tonight against Real Madrid in their Club World Cup opener.