Unite national officer Steve Sibbald explained that the new agreement concerned one and a half weeks' actual pay.
He said: "The company improved its offer on the redundancy pay and staff have voted to accept it. It's an improvement – the original offer was statutory redundancy terms."
Earlier this month, Wyndeham Press Group won IPC Media's print tender for the bulk of its Southbank and Inspire titles, following the printer's acquisition of Southernprint in July last year.
Sibbald said: "I'm certain that the company improved the offer as they didn't want to jeopardise the IPC contract.
"We know IPC had told Southernprint they were nervous about possible industrial action."
Industrial action at Southernprint had looked increasingly likely after staff voted for a second time in favour of a ballot on industrial action in January this year.
Employees had been unhappy since former owner Newsquest "unilaterally changed" the terms of employment, reducing their redundancy entitlement, prior to the printer's sale to Wyndeham Press Group owner Walstead Investments.