The Magpies triggered their option to sign the 26-year-old on a permanent basis following his impressive loan spell during the second half of the season.
Villa will now seek a replacement to provide cover and competition for £25million January signing Lucas Digne. Several targets have been scouted with the club wanting a young, up-and-coming player who can develop as understudy to the France international.
Targett, who joined Villa for an initial £11m in 2019, started the season as first-choice but did not make an appearance after Digne’s arrival from Everton.
He is unlikely to be the only departure from Villa Park this summer with the club willing to listen to offers for fringe players including Anwar El Ghazi and Trezeguet.
Midfielder Douglas Luiz, who has just one year remaining on his contract, has been attracting interest from Roma.