The left-back joins Steven Gerrard’s side in a deal rising to £25million after falling out with the Toffees boss in recent months.
Digne, who moved to Goodison Park from Barcelona in August 2018, said in a post on Instagram on Wednesday evening he has “loved to be a part of the Everton family”.
Benitez confirmed last week the 28-year-old had said he no longer wanted to play for the club.
Digne added: “Only one year ago I signed a new contract with the ambition of staying in this club for a long time, giving everything for my club, for the development and project, that I believed in – and for the passionate fans.
“My dream was helping the club back where it belongs. Wearing the captain’s armband in some matches always made me proud.
“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. But I will not enter a war on words with anyone.”
A lengthy statement ended with: “Sometimes it only takes one person from outside to destroy a beautiful love affair.”
The defender had not played since the Merseyside derby defeat on 1 December after a fall-out with the manager over tactics and his role in the team.
Benitez was critical of Digne’s attitude, saying: “We are paid big money to do our job and if someone is happy or not happy it is (still) up to you to perform in your job.
“You have to put your interests behind the interests of the club. If you are not thinking about that the priority is you and not the team.”
The French international becomes Villa’s second January signing after Philippe Coutinho’s loan arrival from Barcelona.
Villa boss Gerrard told the club’s official site: “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.”
Villa winger Anwar El Ghazi could yet move to Goodison Park but the deals are not linked.
Register for free to continue reading
Registration is a free and easy way to support our truly independent journalism
By registering, you will also enjoy limited access to Premium articles, exclusive newsletters, commenting, and virtual events with our leading journalists
Already have an account? sign in
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies