Inter Milan are paying a fee of around €30m (£25.6m) for Spence, who becomes the second England international to join the Serie A champions this summer after John Stones's free transfer arrival from Manchester City.
Spence had all but confirmed the move earlier on Saturday with a farewell message posted across his social media accounts.
"A special chapter comes to an end," he wrote. "It's been some journey, with plenty of memories, moments and experiences that I'll carry with me for forever, especially that night in Bilbao.
"Thanks to all the staff members who've helped me along the way, the players who've become family and most importantly thank you to the fans.
"Time for a new chapter now, but Spurs will always have a place in my heart."
Spence featured in all eight of England's matches at this summer's World Cup as Thomas Tuchel's side finished third, and made 44 appearances for Spurs in all competitions last season.
His path to regular football at Tottenham had narrowed since Pedro Porro signed a new contract in June and left-back Andy Robertson arrived from Liverpool, with manager Roberto De Zerbi having said in July that he wanted to convince Spence to stay.
He joined Tottenham for an initial £12.5m from Middlesbrough in 2022 and went on to make 85 appearances for the club, helping Spurs win the Europa League in 2025 — the trophy referenced in his farewell message, with the final having been played in Bilbao. This will be Spence's second spell in Italian football, following a six-month loan at Genoa in 2024, and completes a piece of transfer business first reported in an earlier round of speculation linking him with a move to Inter.
The move continues a busy summer at San Siro, with head coach Cristian Chivu also having overseen deals involving Marash Kumbulla and an ongoing pursuit of Liverpool's Curtis Jones.
Spence adds further competition and versatility to Inter's defensive options, having played across multiple positions during his time in England, and gives the Serie A champions a squad increasingly shaped by Premier League recruitment this summer.