Gray has penned a deal to 2030 with Spurs and leaves Elland Road for a fee of £35m.
“It's obviously a massive club and an opportunity I couldn’t really turn down,” he told Tottenham's website. “I'm just really excited to play and get started with the team.
“It still hasn't sunk in, to be honest, and I don't think it will for the next few days and until we have played a few games and until I got to meet everyone. I'm just really excited and looking forward to it and it's a massive opportunity for me.
“When Spurs came and I had the opportunity to play in the Champions League eventually and the Europa League this year, I couldn’t say no. I know so many players here, not so much the first team, but the young lads and obviously another thing, it's a massive project under Ange (Postecoglou) and something I want to be part of.
“Part of the Premier League would suit me more than some of the Championship would and I think I'm ready for it.
“The fitness side of it suits my game so much and the technical aspects of it really suit me as well.
“Quite a lot of it suits me, but there's obviously loads of things I need to start learning and I need to do it in pre-season and I need to get ready for a different league and I need to get ready for that. I'm hoping I'll be able to learn really quickly and perform to my best every game.”