The two new appointments replace HSW Print's Malcolm Hackman and Charles Jarrold of Southernprint, which was acquired by Walstead Investments, which also owns Wyndeham, last month.
BPIF chief executive Michael Johnson welcomed the two "extremely talented individuals" to the board.
"Both gentlemen have a fantastic track record of running successful companies and I know that we shall benefit hugely from the knowledge and insight they bring," he added.