The 40-year-old joins Villa from FC Copenhagen and replaces Jesus Garcia Pitarch, who left on Monday.
With the transfer window open, Villa were keen to make a quick appointment and have turned to Lange, who was assistant to Stale Solbakken during his brief reign at Molineux between 2012 and 2013.
The pair then took over FC Copenhagen before Lange stepped up to the role of technical director at the Danish club in 2014.
Under his watch, Copenhagen have enjoyed a period of domestic dominance while also earning a reputation for signing players on small fees before selling them for major profit.
In a statement, Villa's owners Nassef Sawiris and Wes Edens described Lange's appointment as a "great opportunity" to strengthen the club's recruitment department.
Villa preserved their Premier League status by a single point after a nail-biting final day draw at West Ham.
The statement said: “We’re pleased to welcome Johan to Aston Villa as we continue building a world-class organisation.
“This past season we were able to navigate a very difficult transition into the Premier League and are happy with the effort to stay up. But we will not be satisfied until we achieve our goal of bringing sustainable success to Aston Villa at the top tier of European football.
“We’ve made some significant strides in building an organisation and culture that will sustain success. We made significant investments into our academy programme by upgrading our facilities and bringing in a talented leadership team. We have also significantly invested in our women’s team who achieved promotion to the top tier of women’s football.
“This is a great opportunity to improve our football operations. We’re excited to work directly with Johan and the team to strengthen our analytics, sports science, talent recruitment and player development programmes.
“We are incredibly optimistic about the future of Aston Villa and remain committed to further invest in the club’s success.”
Lange added: “Aston Villa is one of the most famous clubs in European football with a rich history, but it is also a progressive club looking to the future. I am excited and honoured to be given this opportunity to contribute to the club’s ambitious strategy to become a force in Premier League football again.”