The move is subject to the 28 year-old left-back securing a work permit, but as a regular at international level with Sweden, that is not thought to be an issue.
Augustinsson joined Sevilla from Werder Bremen last August.
Although he was never considered a first-choice pick in Andalusia, Augustinsson did manage to make 27 appearances over the course of the season as a back-up to the injury-prone Marcos Acuna.
However, only nine of those outings were as a starter in LaLiga, and his future in Seville never looked entirely secure given Julen Lopetegui often opted to play central defender Karim Rekik ahead of Augustinsson at left-back.
Reports suggest the total value of the deal – including the purchase option – is £3.8million (€4.5m), and the expectation is Augustinsson will be the understudy to France international Lucas Digne.
Augustinsson is the second player to swap the Ramon Sanchez-Pizjuan for Villa Park this year after Diego Carlos.