Gerrard, former Liverpool captain, led the Rangers to the Scottish Premiership title, a first title, in 10 years last season. The 41-year-old replaces Dean Smith who was axed after a run of five consecutive defeats.
Currently, Villa are 16th in the Premier League and only two points above the relegation zone.
“The 41-year-old has attracted many admirers in the game for his work in transforming the fortunes of the Glasgow giants while also implementing an attractive, attacking style of football,” Villa said in a statement.
Gerrard, who enjoyed a glittering playing career with Liverpool and England, joined Rangers in 2018 following a spell as an Academy Coach at Liverpool.
CEO Christian Purslow said: “The Board of Aston Villa are delighted to appoint Steven as our new Head Coach.”
Gerrard after moving into coaching began by managing and developing top young players in the Liverpool FC Academy which we value highly at Aston Villa.
“He then took the brave decision to test himself in the intense and high pressured environment of the Scottish Old Firm. His subsequent achievement in winning the Premiership title with Glasgow Rangers really caught our eye as did his experience in Europe.
“It has been very clear in our discussions with him that Steven’s coaching ambitions, philosophy and values entirely match those of Aston Villa.
“We are excited he has agreed to lead us in the next phase of our ambitious plans as we look to build on the progress made since Nassef Sawiris and Wes Edens took over the club in 2018.”
On the appointment, Steven Gerrard said: “Aston Villa is a club with a rich history and tradition in English football and I am immensely proud to become its new Head Coach.
“In my conversations with Nassef, Wes and the rest of the Board, it was apparent how ambitious their plans are for the club and I am looking forward to helping them achieve their aims.
“I would like to express my sincere gratitude to everybody associated with Glasgow Rangers for giving me the opportunity to manage such an iconic football club. Helping them secure a record-breaking 55th league title will always hold a special place in my heart. I would like to wish the players, staff and supporters the very best for the future.”