The 21-year-old winger completed a permanent move to the KC Stadium during the January transfer window after taking in two successful loan spells with the Tigers.
He admits he found it difficult to turn his back on United, having come through their academy system, but feels regular football at a competitive Championship club will help to keep him in the Republic of Ireland squad.
Brady is hoping to be capped by his country for a fifth time when Ireland face Poland on Wednesday and acknowledges that he has to be catching the eye at club level if he is to remain in Giovanni Trapattoni's thoughts.
He said: "I have always been a Manchester United fan and I always will be. I love the club.
"But it was just the right time for me to get out and play. I need to be playing every week, especially if I want to stay in the international set-up, so it was the right move.
"Obviously, part of me is disappointed and thinking, 'What if?', but you go away and play and work your way back to the top."
Brady scored on his senior international debut in a friendly against Oman in September 2012, and has figured in each of the three games Ireland have played since.
Indeed, Trapattoni turned to him in his hour of need when, after a 6-1 World Cup qualifier drubbing by Germany in October, he handed him a start in the 4-1 defeat of the Faroe Islands in Torshavn amid a frenzy of speculation over the manager's future.
Brady said: "I had been playing well before that and to have his trust put in me, it was brilliant for me.
"I was over the moon when I got the nod. Although I thought I could have played a bit better at times, I was still happy with the start.
"I know he's got faith in me, so hopefully I can repay that by playing well.
"It's all I have ever dreamed about, playing for my country at home, especially. I am really enjoying it. It's hopefully the start of more things to come."