Villa have seen off competition from a host of top clubs to sign the player from Everton and it continues a busy January window for the Midlands club as they brought in Philippe Coutinho on a loan deal from Barcelona.
Digne admits the appeal of working under Villa boss Steven Gerrard was a key factor behind his move.
The full-back told the club's website: "I came here for the manager.
"I had a very good meeting with him, and we spoke a couple of times during this month. I feel his desire to win, to show his football as a manager - the attacking football, the possession.
"I feel it's what I want and what I want to show to the fans."
Gerrard added: "When Lucas became available we jumped at the opportunity to bring him to the club.
"To sign a player of his pedigree and quality in the January window is a great addition to our squad and his arrival excites me and everyone associated with Aston Villa."
Digne appeared to take a parting shot at Everton boss Rafael Benitez as he posted a farewell message for the club's supporters, as the pair's relationship is said to have broken down.
He wrote on Instagram: "Everything must come to an end. I just did not expect it to end this way. What has happened and some things that was said about me in the last month has made me very sad.
"I will always carry you with me in my heart wherever I go.
"Sometimes it only takes one person from outside to destroy a beautiful love affair."