The Colombia international joins Paul Lambert's side on the eve of their opening game of the Premier League season at Stoke City as they look to improve on a 15th-placed finish in 2013-14.
And the 28-year-old admitted he is looking forward to plying his trade in England after seeing compatriot and former Villa striker Juan Pablo Angel succeed on his arrival in the Midlands.
"I'm delighted to be here, it's something I have always dreamed of and it is very important for me to be here at Aston Villa, not only for me but for my family as well," he told the club's official website.
"It was always my aim to play in this country and in this league and I know Villa well as Juan Pablo also played here. I began to watch Villa games when he came in 2001. He was a goalscorer who was very important to this club and I followed his time here because he was always scoring goals."
Lambert has praised the midifielder's eye for a tackle as he looks to add some steel to his side ahead of the new season.
"He does the simple things really well and he's excellent at spotting the danger, dealing with it and keeping it simple. His physical strength, too, is something we will benefit from in the middle of the pitch and his role will be a really important one for the team," he said.
"We've beaten other teams to bring him here to Villa and I'm delighted as we needed someone of his ilk to come in. He'll be an excellent player for the club."
Sanchez started four out of five games for his country in the World Cup in Brazil and moves to Villa Park after just one season in La Liga with Elche.