The veteran defender has left on a free transfer after rarely featuring under Spurs boss Jose Mourinho, who replaced Mauricio Pochettino in 2019.
In a post on Instagram, the Belgian star said: "So my time at the club comes to an end, a sad day for many reasons.
"I will miss the friends I've made here, the staff that make the club run, playing at the amazing new stadium and of course you fans.
"Thank you for all the support over the years. You've been amazing. We had many unbelievable memories but for now, it's goodbye."
Vertonghen, 33, joined Tottenham from Ajax in 2012 and made 315 appearances for the club.
England striker Harry Kane has paid tribute to the defender and goalkeeper Michel Vorm, who is also leaving, on the photo-sharing platform.
He wrote: "Wish nothing but the best for @jvertonghen and @mvorm with whatever is next for them. Been a pleasure sharing a dressing room and playing with them both. (sic)"
Meanwhile, Mourinho has insisted he's planning to take Spurs back "where we belong" after they qualified for the Europa League.
He said: "When all the players are available, we showed in this last period where we belong.
"I don't know, maybe in this period, after lockdown, we finished third or fourth in the table. So that's where we belong. I want to have my team, my players, not a medical room full of players. I want a pitch full of players.
"Of course as a squad, the main thing is to keep our very good players and after that improve the squad.
"Are we going to buy 10 players? No. Are we going to buy players for £100 million? No. We are going to improve."