The midfielder, 28, arrived at Villa Park last week from Elche on a four-year deal.
The Premier League club are understood to have paid around £4m for Sanchez's services.
"I am delighted to be here. It means a lot to me to come here," he told Villa's official website. "I have always wanted to play in England, particularly for a club like Villa.
"As soon as I found out Villa were interested, I had no doubts. I am going to try my very best to grow with the club. It's a big club. I'm sure I can progress here."
Villa continue their Premier League campaign on Saturday when they entertain Newcastle United.