The 27-year-old arrived alongside Atalanta BC teammate Cristian Romero on loan in the summer of 2021, and Spurs possessed the option to make his deal permanent at the end of the season.
Gollini enjoyed regular minutes in the EFL Cup and Europa League for Tottenham, but the Italian consistently struggled to get the nod over Hugo Lloris in the Premier League.
Gollini did not play a single Premier League game for Antonio Conte's side in 2021-22, although he admitted that he would have been prepared to stay in North London for a little while longer.
"Satisfied with the experience? It's normal that I was hoping to play a bit more, but I knew from the beginning that I would play the cups and Lloris the league," Gollini told the DAZN Talks podcast.
"I was playing the Conference [Europa Conference League], and we went out without having played; we had nine cases of Covid, and they didn't let us postpone the game. Carabao? Out in the semi-final with Chelsea and then in the FA Cup, the last one, the coach decided not to do any turnover.
"I played 11 games and was lucky enough to train with Lloris. You can grow even if you don't play, although there are things you only learn on the pitch, like the mistakes you make to improve.
"If you have the right head, even observing certain environments, you can learn. In football, as in other environments. I always thought that you have to make the best out of the situation. If you have the idea of wasting time, you always lose it.
"What future for me? I tell the truth: if I could, I would stay at Tottenham, I feel very good here; I am very attached to this group and the club. If they decide to keep me, I will be happy to stay. Otherwise, if we split up, I would like to go back to Italy. I love my home, the Serie A. Right now, I don't know anything yet."
However, Spurs have now confirmed that they will not be taking up their option to make Gollini's deal permanent, and the one-cap Italy international will be heading back to Atalanta.
The former Manchester United and Aston Villa prospect leaves the club having made 10 appearances in all tournaments, keeping two clean sheets in the process.
Gollini headlines a double-figure list of players to leave Tottenham, with J'Neil Bennett, Kacper Kurylowicz, Dermi Lusala, Thimothee Lo-Tutala, Josh Oluwayemi, Tobi Omole and Isak Solberg all departing the development squad.
Furthermore, a quintet of Under-18s players in Jez Davies, Jordan Hackett, Khalon Haysman, Renaldo Torraj and Oliver Turner are also on their way out after their scholarship deals ended.
Tottenham are set to replace Gollini with Southampton goalkeeper Fraser Forster, who is understood to have agreed terms on a two-year contract with the Champions League contenders.
Spurs have already announced the capture of Ivan Perisic on a free transfer from Inter Milan, while official confirmation of Forster's arrival is expected in the coming days.
Conte is also keen to improve his backline with the acquisition of Nerazzurri centre-back Alessandro Bastoni, and a recent report claimed that the Lilywhites have also been offered the chance to sign West Ham United midfielder Tomas Soucek amid uncertainty surrounding Harry Winks's future.