Brevett, 35, was released by the Hammers at the end of the last season after losing his place in the side to Chris Powell.
Rufus joined West Ham in a £375,000 switch from Fulham in January 2003 and made 29 starts for the club.
He joins Anthony Barness, Bojan Djordjic and self-reported Hammers target Akos Buzsaky as Argyle’s forth signing of the new season.