According to Sky Germany, the 31-year-old midfielder successfully completed his medical with Villa on Tuesday, with an official announcement of the signing expected shortly.
Goretzka has been a free agent since his Bayern Munich contract expired at the end of last season, and had been linked with a wide range of clubs in recent weeks, including Arsenal, AC Milan and Barcelona, before opting for a move to the Premier League.
The Germany international, capped 73 times by his country, spent eight seasons at Bayern, making more than 300 appearances and winning seven Bundesliga titles alongside the Champions League and numerous domestic trophies.
His arrival at Villa Park is designed to provide cover following Amadou Onana's serious knee injury, sustained playing for Belgium at this summer's World Cup, which is expected to rule the Belgian out for the majority of the season.
Aston Villa manager Unai Emery is understood to have played a personal role in persuading Goretzka to choose Villa over his other suitors, contacting the midfielder directly to outline his vision for how he would be used. The move represents a notable coup for Villa given the level of interest Goretzka attracted elsewhere, with the free transfer nonetheless expected to carry a significant wage package befitting a player of his pedigree and World Cup-winning experience.
Goretzka is set to sign a contract of two to three years and could feature for Villa as soon as their Premier League match against Arsenal, giving Emery a considerable boost to his midfield options as the transfer window enters its final week.
Villa's summer has been defined as much by departures as arrivals, with the club losing key figures including Morgan Rogers and Youri Tielemans, while also navigating restrictive financial regulations that have complicated efforts to strengthen elsewhere.
Signing a player of Goretzka's calibre on a free transfer, even accounting for the wage outlay involved, represents one of the more efficient pieces of business available to Villa given those constraints, offering physical presence, leadership and Champions League pedigree to a squad that has needed reinforcement in central midfield since Onana's injury.
The move also caps a frustrating summer for Goretzka himself, who spent seven weeks as a free agent before agreeing terms, with reports suggesting his wage demands — believed to be in the region of €7million a season plus a substantial signing bonus — had deterred several of his other suitors from following through on their interest.