The 24-year-old has agreed a four-year deal with the French club, with whom he spent last season on loan, after the clubs agreed a fee thought to be in the region of £4.5million.
Veretout was named on the bench on the official team sheet for Tuesday night’s friendly at Walsall but was not present at the Banks’s Stadium and will become the second departure from Villa Park this summer after Carles Gil’s loan move to Deportivo earlier this month.
Villa splashed out £9million to acquire Veretout’s services two summers ago, seeing off competition from Leicester City.
But he struggled to make an impact during the 2015-16 campaign which ended in Villa’s relegation from the Premier League.
Veretout made clear his desire to leave last summer and eventually joined St Etienne on loan, playing a part in the club’s Europa League campaign.
Villa are expected to complete the signing of wideman Ahmed Elmohamady from Hull City on a £1million deal on Wednesday.