The retired Germany international replaces Michael Reschke, who left the former national champions after just 18 months in the role.
Hitzlsperger made 108 appearances for Villa between 2000 and 2005 after joining from Bayern Munich, scoring 10 goals and registering one assist, according to Transfermarkt.
The 36-year-old, who plied his trade in midfield, also played for Chesterfield, West Ham United and Everton in England, as well as turning out for Wolfsburg in Germany and Lazio in Italy.
However, it is at Stuttgart where Hitzlsperger picked up medals, lifting the Bundesliga title in 2006-07 and finishing runner-up in the German Cup the same season.
"I will do my utmost to concentrate our strengths so that we stay up and at the same time set a course for a successful future," Hitzlsperger is quoted by BBC Sport as saying.
Stuttgart, who have won five German top-flight titles in their history, are currently 16th in the Bundesliga table - the relegation/promotion playoff place - having picked up 15 points from 21 league fixtures so far.
Markus Weinzierl, the club's second manager of the season, has lost 10 of his 14 games in charge and remains under pressure ahead of their home game against RB Leipzig next weekend, according to ESPN.