Heineken, which also owns the Strongbow and Foster's brands, is paying £305m to swallow up 1,900 pubs, while partner Patron Capital will take on 1,300.
The agreement saw the bidders fight off a rival proposal from Punch co-founder Alan McIntosh.
Punch's top three shareholders, representing 52% of its shares, have backed the Heineken offer.
Details of the takeover battle were first reported by Sky News.
Heineken, subject to approval by regulators, will add the pubs it is acquiring to the 1,100 it already owns through its Star Pubs & Bars business.
David Forde, Heineken UK's managing director, said: "Today's announcement is a huge vote of confidence in the great British pub."
He told Ian King Live this was a "growth story" for the company despite the pub industry's notoriously high cost base.
Patron said it expected to pursue key elements of the current Punch management team's strategy.
Punch chairman Stephen Billingham said it was "a good outcome for shareholders" with the offer at a 40% premium to its market value prior to the takeover attempt being disclosed.
The company last month reported its first annual profit since 2013, and said that it had reached the conclusion of a disposal programme aimed at reducing its huge debt pile.
The improvement in its financial performance under new chief executive Duncan Garrood comes after years of complex restructuring which included a demerger of Spirit, the managed pubs company which was later bought by Greene King (Frankfurt: A0F66P - news) .
Punch shares closed 7.9% higher on Thursday.