Pitarch, known as "Suso", joined Villa in October 2018, but he came under fire after the club only narrowly avoided relegation despite spending in excess of £140 million ($253.4 million) after its promotion from the EFL Championship last year.
Villa announced Pitarch's departure on Wednesday (AEST), and has moved quickly to bring in his replacement.
Lange joins from Copenhagen, having served as the Danish side's technical director for the past six years.
"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," Lange said.
"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."
One of Lange's first tasks could be to replace Jack Grealish, with Villa's captain having been heavily linked with a move away.