The 30-year-old will join the Easter Road club this summer when his deal at McDiarmid Park expires.
Swanson, who spent five months with Hearts last season, has scored 13 goals this term to help St Johnstone into fourth place in the table.
Saints manager Tommy Wright was eager to keep his talisman, while Aberdeen had also shown an interest in securing his services for next season.
However, the former Berwick Rangers, Dundee United, Peterborough and Coventry City player has chosen to pledge his future to Hibs, the club he supports.
The deal is done and will be confirmed by the Easter Road club in due course.
Neil Lennon’s side have also been linked with a move for ex-Charlton striker Piotr Parzyszek, a Polish under-21 international who’s scored regularly for De Graafschap in the Dutch second tier.
The Daily Record claim Hibs are ready to swoop for him this summer when his contract expires in the Netherlands.