The Viola chief says the chance of the Colombian midfielder joining Barcelona, Manchester United or Bayern Munich this summer have passed and he will remain in Serie A
The Catalan giants were leading the race for his signature for months but were reported have been put off by his high price-tag and instead chose to sign Douglas Pereira from Sao Paulo to fill the void on the right flank of their midfield.
Earlier this month Goal reported that Manchester United had held talks with Fiorentina over a £35 million deal for Cuadrado, while Bayern Munich were also linked with a possible move.
On Monday the 25-year-old suggested he was still open to a summer transfer, but Della Valle now insists his star man will be staying at Artemio Franchi.
"I can guarantee that Cuadrado is certainly staying," Della Valle told reporters. "It's a huge gift for the city. I hope it's the strongest Fiorentina in my era in charge."
Montella also expressed his delight that the in-demand 26-year-old will not be leaving the club ahead of the 2014-15 season and is looking ahead to Fiorentina's opening game of the Serie A season at Roma on Saturday.
"I am happy, very happy indeed," the coach added. "Cuadrado's an important player for Fiorentina.
"Tomorrow begins a whole new season of expectation. There are no assumptions but there is a belief that must be turned into positive results.
"Roma are among the favourites with Juventus and Inter, whom I think are looking strong. Serie A's a league which looks stronger."