Tottenham signed Tonali from Newcastle United during the summer for a club-record £92.5 million plus £7.5 million in add-ons, with the Italy midfielder agreeing to a six-year contract.
Manchester City had also been interested before turning their attention to Elliot Anderson after missing out on Tonali.
Riso revealed that he took responsibility for convincing his client to move to north London after explaining the options available to him.
"It was a crazy move in terms of the noise, the numbers, and the responsibilities," Riso said on the Colpi Da Maestro podcast.
"I explained things to Sandro, I made him think, and I took responsibility. It turned out to be the right choice, even from a personal perspective, even though cycles end and we decided to leave."
The agent also explained why Tottenham ultimately won the race for Tonali.
"After Newcastle, Tottenham showed they're choosing differently; they're courageous," Riso said.
"Tottenham was reborn after the end of the season; Tottenham survived, and De Zerbi came to the house, telling him they needed him as a leader. The relationship with De Zerbi carried a lot of weight."
Tonali spent three seasons at Newcastle after joining from AC Milan for £55 million in July 2023.
Riso was also involved in the midfielder's original move to England and explained why Tonali eventually decided to leave Milan despite being captain of the side that won the Serie A title.
"The first move was because we had the feeling that it was a different Milan. I know Milan inside and out, Sandro thought about it.
"He understood he wanted to join that kind of football, the Premier League. Sandro was intrigued by that choice, even though he was the captain of the Milan team that had won the Scudetto.
"It was extremely difficult for him, but he was a visionary; little by little, he got the hang of it, and then he established himself."
Tonali has started all five of Tottenham's Premier League matches this season but has yet to make the desired impact as Spurs sit bottom of the table.
The midfielder will now be expected to play a leading role as De Zerbi attempts to turn Tottenham's difficult start around.