Writing in today's match programme, Levy laid out plans to build on a first European trophy in 41 years.
Ahead of their clash with Brighton, the chairman wrote: "We did it. What an unforgettable night it was in Bilbao as we ended our long wait for glory.
"This is a huge moment for the whole Club, an historic achievement that sees us lift our first European trophy since 1984.
"This Club has been on an incredible journey on and off the pitch since we last won silverware, the League Cup, in 2008 – establishing ourselves as one of the biggest in Europe, moving into our new stadium and experiencing some incredible moments – we knew a trophy was the missing piece.
"We’ve come so close on a number of occasions and never quite got over the line – I have never wavered from the belief that success is just around the corner."
Thank-you Ange
Levy also stated: "I’d like to thank Ange and the players for making this incredible achievement possible and thanks to all of our amazing staff – there is so much hard work that goes on behind the scenes and this moment is for everyone to enjoy.
"I’d also like to thank you – the fans – for staying with us and carrying that same belief. I know it’s been hard at times and I have shared in that pain and frustration along the way. But when we all come together, we know we can achieve something special.
"Your support – whether that was in Bilbao, in our own stadium or in pubs and homes around the world – was the driving force behind our team.
"This is one trophy – our clear ambition as a Club has always been long-term, sustained success, competing for top honours every year. We have now tasted success and we are determined to use this as a springboard for more.
"Let’s enjoy this moment as a Club together, finish the season strong with a win today and go again next year.
"Most of all, be proud. Come on you Spurs! Daniel.”