The left-back has been an influential figure for Everton over the past four years.
But he fell out of favour this season under manager Rafael Benitez, who said last week Digne had asked to leave the club.
Several teams registered their interest in the defender, including Newcastle, Chelsea and sides from Serie A – but it was Villa who were successful in securing his signature in a £25million switch.
Digne’s last game for Everton was on December 1 due to his fallout with Benitez.
But he says he is ready to play if Steven Gerrard wants to use him against Manchester United.
“Villa Park is an amazing stadium,” the Frenchman said.
“The fans make noise, it’ s magic stadium.
“And that first game is going to be a big moment.
“It (Manchester United) will be a big game, a big first game for me too if I have the opportunity to play. I can’t wait.”
Digne was given a guided tour of Bodymour Heath by Gerrard yesterday.
And the full-back was hugely impressed by Villa’s Bodymoor Heath training ground.
“It’s massive,” he continued.
“The training ground is amazing.
“It’s modern. The club has everything you need to improve.”
Everton signed Digne from Barcelona in the summer of 2018 for £18m under former manager Marco Silva.
He went on to make 127 appearances for the Goodison Park club, scoring six goals.
And the France international – who has won 43 caps for his country – took to social media to express his surprise at how his time with the Toffees ended.
“What has happened and some things that was said about me in the last month has made me very sad,” Digne wrote on Instagram.
“But I will not enter a war on words with anyone.
“The club don’t deserve that, the fans don’t deserve that – and to be honest, I don’t feel that I deserve that.
“Sometimes it only takes one person from outside to destroy a beautiful love affair.”
Digne is Villa’s second signing of the January transfer window following the arrival of Brazilian playmaker Philippe Coutinho.
And Gerrard admitted he is delighted to have the full-back on board, with Digne set to compete with Matt Targett for the left-back spot.
“When Lucas became available we jumped at the opportunity to bring him to the club,” the boss said.
“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.”
n Anwar El Ghazi has moved to Everton on loan until the end of the season.
El Ghazi has been at Villa since 2018 and scored in the play-off final victory over Derby that secured the claret and blues’ return to the Premier League in 2019.
“I’m really excited. Everton is a big club, I cannot wait to get started,” El Ghazi said. “I want to show my quality to my teammates, to the club and, of course, the fans. I want to put a smile on their faces.”