The former Liverpool captain, 41, leaves the Scottish champions having guided them to a first league title in 10 years last season.
Gerrard replaces Dean Smith, who was sacked on Sunday after a run of five successive defeats.
Villa are 16th in the Premier League, two points above the relegation zone.
"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.
"In my conversations with [co-owners] Nassef [Sawiris], Wes [Edens] 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."
BBC Sport Scotland reports Villa have paid Rangers £4.5m in compensation.
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