The increase is applicable to all levels of pay in the industry and extends to shifts and overtime.
Unite said it would recommend the deal to workers, who will vote on 12 March.
The BPIF will also receive feedback from its members during this period.
If the agreement is voted through, companies would be expected to implement the increases on 24 April.
BPIF corporate affairs director Andrew Brown described the negotiations as "a mature dialogue".
"It's the most important thing for the union and it's critically important to our members," he said.
He added that the cash settlement isn't a flat percentage increase. "We want companies to work out for themselves the impact of the increase on their wage bills."
He said some of this could be offset through cost recovery initiatives.
Unite assistant general secretary Tony Burke said: "Given the current difficulties within the printing industry, we believe this is the best that can be achieved by negotiations."
BPIF chairman of the negotiating panel Dominic Walsh said: "This is a fair deal for our industry. The reaffirmation by Unite the union of continuous improvement/cost recovery is a key element of this proposed pay award."
Brown said that although consolidation had taken some pressure off overcapacity within the industry, the rationalisation looked set to continue and that companies remained under pressure.
"There will be companies that can't afford to pay the full increase," he told printweek.com. "What we would say is that such a company should contact the union and the BPIF well in advance of the 24 April implementation date."
He warned: "I daresay that there will be some companies that still won't be able to make that commitment."
Got an opinion? Have your say on the pay increase agreement by voting in our poll on the left of this page.