The winger attracted interest from a number of clubs, including the Serie A side, before deciding to sign with last season's FA Cup finalists.
Livermore, who made the permanent move to Hull earlier this summer after a loan spell at the club, told Perform: "It's a great opportunity for him to come here and play Premier League football. He's got great talent and to share that here with us and progress would be great.
"I've had so many people when I made it apparent I wanted to join Hull saying, 'There's bigger clubs you could join'. At the end of the day, if a player is happy with where he wants to go, happy with the manager and has a good set of lads around him, that's what it's about.
"It's also about challenging yourself in life sometimes. If I wanted the easy option I could have stayed at Tottenham and seen the rest of my three or four years out that I had. For me, I wanted to be part of something and obviously help Hull City and me go in the right direction, which is up."
Ince spent the second half of last season on loan with Crystal Palace.