Lambert joins from Norwich City, having offered his resignation earlier in the week, after leading the Canaries to a very respectable 12th place on their return to the top flight last season.
The 42-year-old Scot was reported to have signed a three-year deal with the 1982 European champions, who were founder members of the Football League in 1888 and last won a league title in 1981.
Liverpool, five times winners of Europe's top club trophy but without a league title since 1990, named Swansea City boss Brendan Rodgers as their new manager on Friday.
Both clubs have small grounds, Swansea's capacity is only 20,000, but their attractive style of play caught the eye of American owners at the two former European Cup winners.
"The Board of Aston Villa are delighted to confirm that Paul Lambert has been appointed Villa manager," it said.
"Just to stop the rumour mill again. I have expressed to the board and the CEO that I want to leave the football club. Due to disagreements," Holt said on social media site Twitter on Friday.
"As a player, he always thought like a coach. He was a leader. He didn't cost a fortune when I bought him, and no one expected him to become a key player but he did," said Hitzfeld. "So it is no surprise that he has become a successful manager."
Villa's American chairman Randy Lerner said last month that the Birmingham-based club lacked the sort of "compelling play" the fans expected.
Lambert, a player under former Villa manager Martin O'Neill at Celtic, will be expected to deliver as he becomes the fourth man in charge at Villa in less than two years.
