A product of Chelsea's academy, Iling Junior leaves Juventus after a four-year stay. Iling-Junior, who has represented England at the Under-21 level, won the Coppa Italia last season with the Turin-based club.
Argentine Barrenechea started his career at Newell's Old Boys before moving to Swiss side Sion. He spent the last campaign on loan at Serie A's Frosinone.
Neither Villa nor Juventus provided financial details of the deal.
The signings come a day after Juventus signed Brazilian midfielder Douglas Luiz from Villa on a five-year deal.