Radrizzani had bought 50% stake in the club back in January, and on Tuesday, he announced the purchase of the remaining 50% from his compatriot Massimo Cellino.
Radrizzani told the club website: "I am delighted to have the opportunity to become a custodian of this great football club.
"The heritage and history of Leeds United attracted me to the club and having spent time at games and at Thorp Arch, I can see that we are ready to move forward to the next level.
"This is a long-term commitment, there is a lot of hard work ahead of us and I am aware of my responsibilities as owner of Leeds United.
"I can assure all supporters that everyone at this club will be doing all we can to build a successful team at Elland Road."