Gerrard has left his role as Rangers manager to take charge at Villa, who sacked Dean Smith last Sunday after five successive league defeats.
Considered one of the greatest players in Premier League history, former England midfielder Gerrard made a promising start to his managerial career by reviving the fortunes of the Glasgow giants.
The 41-year-old guided Rangers to a first Scottish Premiership title in 10 years last season, with the club finishing the campaign undefeated in the league for the first time in 122 years.
Gerrard, who took the reins at Ibrox in May 2018, also made progress in Europe, reaching the knockout stages of the Europa League for the past two seasons.
“The board of Aston Villa are delighted to appoint Steven as our new head coach,” said Villa CEO Christian Purslow, who was managing director of Liverpool when Gerrard was at the club.
“Since moving into coaching after his illustrious playing career, Steven began by managing and developing top young players in the Liverpool FC Academy, which is experience 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.”
Villa finished 11th in the Premier League last season, but have ambitions of challenging for Europe after spending nearly £300 million (B13 billion) on players over the past three seasons.
However, Smith paid the price for losing Jack Grealish to Manchester City in August in a British record £100 million deal, with new signings Danny Ings, Leon Bailey and Emi Buendia struggling for form and fitness.
Villa are languishing in 16th place in the Premier League, two points above the relegation zone, after 11 games.
Gerrard, who never won the Premier League title as a player with Liverpool, is widely expected to return to Anfield as manager at some stage but now has the task of proving himself in one of the toughest leagues in the world.
“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,” said Gerrard.
“It was apparent how ambitious their plans are for the club and I am looking forward to helping them achieve their aims.”
Rangers thanked Gerrard for his contribution to ending bitter rivals Celtic’s domination of Scottish football.
The Hoops won the league in Gerrard’s first two seasons in Glasgow to match a record nine consecutive titles, but were blown away as Rangers romped to a 55th title by 25 points last season.
“I would firstly like to put on record my thanks to Steven for his outstanding efforts over the last three-and-a-half years at Rangers,” said Blues chairman Douglas Park.
“He has provided us all with some unforgettable moments, not least his delivery of the Scottish Premiership title back to Ibrox last season having not lost a match in the entire league campaign.
“In European competition, he has restored the good name and credibility of our club on the continent and leaves us in a very healthy position on the pitch.”
Former European champions Villa are one of the great names of English football but have not won a domestic trophy since 1996.
Gerrard’s first game will be at home to Brighton on November 20, following the current international break.
He takes his side to face Jurgen Klopp’s Liverpool on December 11 and also has tough fixtures against Manchester City and Chelsea next month.