Both players sealed their moves to Villa Park on Thursday as Villa boss Martin O'Neill bolstered his defensive options ahead of the new season.
Former Tottenham and Charlton defender Young, 29, has seven England caps but has not featured for the national team since a friendly against Argentina in November 2005.
He could make his first competitive appearance for the Villans in next week's UEFA Cup qualifier against FH Hafnarfjordur, and admits the promise of European football was a major element in his decision to leave the Riverside.
"The chance of European football was definitely an important factor in my decision. You always want to test yourself at the highest level," he told the club's official website.
"I had a brief stint playing European football at Tottenham. But that was almost 10 years ago, and it will be great to get another chance this season.
"It's definitely a case that Villa's ambitions match my own. I've worked hard over the last 10 years to perhaps get this chance to show what I can do on a little bit of a higher stage."
He added: "I'm really pleased to be here at Villa. It's happened quite quickly. One minute I was training up at Boro and the next I'm down here for a medical.
"Obviously I'm glad to be here now, but it could have been a year earlier. There was interest last summer, but it didn't quite happen for whatever reason. I'm just glad to find myself here now.
"I think this is a great opportunity for me to try and win something. I think at the minute Villa are a notch above Boro."
Young spent just a season at Boro after his cut-price £2.5million move from Charlton, following the Addicks' relegation.
He will finally provide Villa with a first-choice right-back after the departure of last year's incumbent Olof Mellberg, who has since left the club for Juventus.
O'Neill added: "The right-back position caused us a few problems for us last season, in terms of us not having a natural right-back.
"Luke is a natural right-back and played for England not so long ago. He did very well for Boro last season, and this is a great opportunity for him."