The Italian goalkeeper revealed that the chance to move to Villa was too good an opportunity to turn down.
Gollini looks set to become Villa manager Roberto Di Matteo's second signing of the summer in the next few days after the addition of Bournemouth captain Tommy Elphick.
A report on Tuesday claimed that the deal for the 21-year-old was "one step away" from being completed for a fee of around £4.25 million, with the player set to sign a four-year deal at Villa Park.
Now, Gollini himself appears to have confirmed the imminent move, telling Sky Italia in an interview at an airport that Di Matteo's desire to bring him to Villa was enough to convince him to make the move.
Gollini said: "I am very happy. I'm sincerely sorry to be leaving my town in Italy but it is a big opportunity for me. I've been to see the stadium of 40,000 people and it is incredible. Aston Villa is a glorious club.
"There were several interested clubs, [but] Di Matteo wanted me strongly and I think it will give me a great opportunity.
"I also thank Verona for getting me to where I am. For the last two years Verona has given me a lot of opportunities. I also want to thank the people of Verona."
Gollini will come in to initially compete with Brad Guzan and Mark Bunn for the number one spot, although it has been speculation that Guzan could leave the club this summer.
Meanwhile, Villa could also be closing in on a midfield addition, with a report earlier this week claiming that the relegated club have had a £5 million bid accepted for Reading midfielder Aaron Tshibola.