Spence completed a permanent transfer from Tottenham Hotspur worth around €30 million, signing a five-year deal that runs until 2031.
The England international arrives as a replacement for Denzel Dumfries, who left Inter Milan for Real Madrid earlier in the summer, and joins on the back of a breakout World Cup campaign in which he started England's semi-final defeat to Argentina and their third-place play-off win.
"This is a great club and a great step for me and my family: I'm proud to be here, as if I was on the Moon. I'm ready to start," the new Inter full-back said, speaking to the club's in-house channels immediately after signing his contract.
Asked what appealed to him most about the move, Spence pointed to the club's history.
"Definitely the club's history, just look at how many trophies there are behind you here. This is really a huge club."
The Englishman reflected on how his time in England, France and Italy has shaped him as a player.
"I think it's shaped me a lot, you learn a lot when you're abroad. Abroad I became a man: I'm grateful for these experiences."
Spence has already experienced Serie A during a previous loan spell in Italy, and was asked what that period taught him that could now be useful at Inter, and what it meant to play at San Siro as an opponent.
"I remember it was a great time, so many legends have played there. I remember it was beautiful and now I'm happy to come back as an Inter player."
He was also asked whether supporters could expect the kind of dramatic intervention he produced for England against Argentina at the World Cup, when he made a crucial goal-line save on Giuliano Simeone.
"Definitely yes, I'm a player who likes to take risks and you'll see me like that at Inter too."
Known primarily for his pace and his ability to attack down the right, Spence was asked to identify his best attribute and where he still wants to improve.
"My defensive ability is my best characteristic, as well as my ability to carry the ball. I'd like to add more goals and assists: if I managed that I'd become a really good player."
The 26-year-old revealed he had yet to speak with most of his new teammates, though he already has connections in the Inter dressing room.
"I haven't spoken to any of them yet, but it's true that I was with Martinez at Genoa two years ago and with Stones at the World Cup, who has sent me messages in the last few days: I can't wait to see them and get started."
Asked for a message to the Inter fans, Spence kept it simple: "Forza Inter!"