Mr Salwai lost his parliamentary seat for Pentecost at the start of the year after being given a two year suspended sentence for a perjury conviction.
However, the President of Vanuatu, Obed Moses Tallis, last week pardoned the convictions of Mr Salwai and two other former prime ministers, Joe Natuman, and Serge Vohor.
The pardons mean they are cleared to stand again for public office.
The Pentcost by-election is scheduled for October.
Mr Salwai's Reunification of Movement for Change party has six MPs in the 52-seat parliament.