Orta was brought in by 'Boro in December 2015 as their chief European scout.
But Orta, who has previously worked at Zenit St Petersburg and Sevilla, had a mixed track record in the transfer market with 'Boro.
Radrizzani, however; is confident he will be a success in West Yorkshire.
"I'm delighted to welcome Victor to Elland Road," said the Leeds owner.
"I have been impressed by his knowledge of the game, his extensive scouting network and his desire to help us achieve our objective of getting Leeds United back to the Premier League."
Orta's arrival points towards Aitor Karanka heading the race for the Leeds head coach role, given that the two Spaniards worked closely together at Middlesbrough before losing their jobs – and a reunion could well be on the cards.