The deal is worth a reported £30 million, as per Sky Sports.
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Villa will pay £25 million plus £5 million in add-ons for the Saints defender.
The 24-year-old has made 121 appearances for Southampton across four seasons, and netted seven times in the English Championship last season.
Villa have been keen to bring in defensive reinforcements following Ezri Konsa's summer move to Arsenal, as they look to improve on a disastrous start to the league season which has left them bottom of the Premier League table.