Nielsen was a big favourite at Villa Park after moving from Brondby in 1989.
"Nicklas has very good vision," said Nielsen to avfc.co.uk. "Last season he was not only our highest scorer, he also made the most assists.
"He is always aware of his team-mates and he has a very good pass.
"He's also very lively during matches and will always cause problems for the opposition.
"He scored a lot of goals at under-17 and under-19 level, and he has continued scoring for the two-and-a-half years I have been at the club.
"I'm pleased he has joined Villa. If he was going to join a Premier League club, Villa were the right club for him.
"That's not just because Villa are close to my heart. They have a very young squad at the moment and they are giving the youngsters a chance, just like we have done here in Aalborg."