The former Leicester City midfielder made the move to Old Trafford last month after United activated his £35M release clause at Villa Park and the Belgium international instantly accepted their offer.
United twice before missed out on a deal to sign Tielemans in his early career and the 29-year-old has signed a contract at Old Trafford until 2031.
As part of his first interview as a United player, Tielemans pointed to the 'gap' between the two clubs, which tipped the balance for him.
"I was not expecting much this summer. I was just focused on my football, focused on the World Cup and trying to perform my best for my country.
"I'm very thankful to Aston Villa. I owe them the world. It's a great club, we did amazing things and they have put me back to my best level. But there are clubs above Villa, and Manchester United is one of them."
Those comments led to criticism over his attitude towards Villa - who join United in the 2026/27 UEFA Champions League - and he's since looked to correct the record.
"I never meant for my words to offend anyone or the institution of Aston Villa Football Club, which I massively respect and I'm grateful for the past three years," he posted on social media.
"I must however admit my mistake and apologise for my choice of words, I will be more careful in the future.
"Wishing the club the best in the future."