Ibrox chairman Sir David Murray revealed at the weekend that Rangers failed in their bid because he was unwilling to blow the club's wage structure in a bid to land the 22-year-old.
But Brown said: "Nobody knows what I'm on. People may think they know what I'm on, but it's totally different. I chose Celtic because I wanted to play for Celtic. They were a dominant force in Scotland last season, they won trophies and got to the last 16 of the Champions League. That's why I want to be here. I want to win trophies here and go as far as possible in the Champions League."
Brown added: "I hope I play every week, I want to play every week. If I don't, I'm going to have to show the gaffer what I'm made of in under-21 games and in training. I've learned under every manager. I learned under John Collins and Tony Mowbray and I will learn under Gordon Strachan as well."