The left-back completed a £10 million move to White Hart Lane on Wednesday, along with goalkeeper Michel Vorm as Gylfi Sigurdsson moved the other way.
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"I had never thought or wanted to leave Swansea, but an opportunity like this doesn't come up often in your career," Davies told the club's official website.
"I will always be grateful for what Swansea City has done for me and it will always be the club in my heart.
"Having been at the club since the age of eight, I had to think long and hard about leaving because I owe everything to the staff and the club in general.
"It's quite ironic really that it was on our last American tour two years ago that I was first introduced into the first team. Then, when Neil Taylor had his bad injury soon after, I found myself a regular in the team.
"It was a massive step for me and it wasn't easy. But the supporters were right behind me from the very start. They believed in me and gave me the backing I probably needed as a young player at the time.
"I'd like to thank them all personally, but obviously that's not possible. Like I said, I'll always be grateful, but I also hope they feel I have given something back to them over the last two years.
"It was sad saying my goodbyes because they've been great with me from the first day I joined the squad. But in the end it was an opportunity I couldn't turn down."
Davies, who ends a 13-year association with the Swans, is confident his fee will be invested to help the improve the squad and is looking forward to the "challenge" of playing for Tottenham.
He added: "Now I'm sure the chairman and manager will use the funds to strengthen the squad and I know they'll make the right decisions in the interests of the team, club and fans.
"Moving to Spurs is a massive footballing challenge for me again. They were the ones chasing me from the beginning and I want to repay their faith ... by doing well for them and continuing to improve as a player."