The 26-year-old front man scored three times over two games as Stratford dumped the Pilgrims out of the competition last season, including netting the Bards' leveller in their 1-1 draw at the Jakemans Community Stadium.
He then went on to have spells with Boston's National League North rivals Hereford and Brackley.
“Having worked with Jaanai before, I am well aware of the qualities he possesses,” manager Paul Cox told bufc.co.uk.
“He has a tremendous work ethic, desire and application.
“Jaanai has the adaptability that we were looking for and with a number of clubs looking to sign him for the season ahead, I feel we have signed a player that will not only score goals, but will create goals for others.”