Attacking midfielder Brown became United's sixth signing of the summer on Thursday evening with the 21-year-old joining goalkeeper Jamal Blackman and midfielder Lewis Baker on loan from Chelsea.
After signing just one day before the closure of the summer loan window, Brown revealed that the first game he had ever watched live had come at Elland Road with the England under-20s star declaring he had joined an "amazing" club upon making the loan switch to West Yorkshire.
"It feels amazing to be part of such a huge club," Brown told LUTV.
"My first ever game I watched live was at Elland Road - Chelsea against Leeds when I was younger.
"In that game, Leeds won, I don't know the score, I think 3-1 or 4-1 or something like that but ever since then I have remembered that atmosphere and I felt the same atmosphere when I was playing for Rotherham against Leeds.
"You can tell the fans are a huge part of this club - it's an amazing club."
“The fans always back the team 110 per cent and they give the team an extra boost on the pitch, they are a huge part of this club and it is an amazing club."
Reflecting on the decision to join United, Brown said: "The decision was easy, I’ve known of Leeds’ interest for around 18 months now and ever since then it has been in the back of my mind.
"It is a huge club with a huge fan base, it has an amazing stadium, an amazing training ground and it is a Premier League club in a way and hopefully that is what we can become.
"I’ve watched every Leeds game on Sky, they have been amazing and you can see the way the manager has got them playing, that is the kind of football I want to play.
"They press high, win the ball back high up the pitch and try to score as many goals as possible, it looks fun and I can’t wait to be part of it.
"I’m so happy to be part of this team and I can’t wait to get out on the pitch and get playing."