Brady helped Hull win promotion to the Premier League after making the move permanent for £2m and has no regrets about quitting the champions.
He told the Daily Star: "I left United on good terms. The six years I was there really helped me as a footballer.
"I wouldn't be where I am now if it wasn't for United and Sir Alex. I enjoyed my time there.
"This is a new chapter. Sir Alex had me playing at left-back and although I'm higher up the pitch now I think it helped me in the long run.
"It's a big step leaving United. I didn't know anything else but them. But it was the right decision and I'm really happy. I left with Sir Alex's blessing.
"He's an inspiration, the best manager ever, and I really enjoyed my time working under him.
"But it was time to move on and things are going well for me now."
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