Dana, which specialises in car part manufacturing, said it had “improved the terms of its agreed combination” by upping the cash offer by 8.6% or 140 million US dollars (£100 million).
It brings the total cash consideration to 1.77 billion US dollars (£1.28 billion).
It will also double the size of its share repurchase programme to 200 million US dollars (£145 million), helping sweeten the overall deal which was previously valued at around £4.4 billion.
GKN welcomed the announcement, which will see its shareholders own more than 47% of the combined company that is set to be listed on both the New York Stock Exchange and London Stock Exchange.
It said £700 million would be returned to shareholders “as soon as practicable” after the deal is completed.
GKN chairman Mike Turner said: “This transaction, which along with Project Boost was initiated prior to the Melrose bid, offers by far the best strategic route forward for GKN Driveline.
“The challenges and opportunities of electrification mean that consolidation is required. By moving now, the Dana-GKN Driveline combination will be strongly positioned to be a global leader in this field.”
He added: “We believe that Melrose would find it extremely difficult to create equivalent value in the future from GKN Driveline if its offer were to be successful.”
The announcement comes just days before GKN’s fate could be sealed as part of a shareholder vote over an £8.1 billion bid for the British engineering firm by turnaround specialist Melrose.
GKN investors have until 1pm on March 29 to cast their ballots on the controversial deal.
GKN has doggedly rejected Melrose’s advances, with chief executive Anne Stevens describing Melrose’s takeover as “high-risk” and the offer not coming close to reflecting true value.
The deal to sell its Driveline division to Dana is part of a raft of counter measures meant to fend off Melrose’s advances - having become a takeover target following profit warnings in October and November after problems at its US aerospace division sent shares tumbling.
Mr Turner added: “GKN has re-invented itself numerous times in its 250-year history.
“We are confident that, following the Dana transaction and the non-core disposals, GKN will become a pure play aerospace company with a strong balance sheet, our pension challenges behind us and a clear plan for delivering leading margin performance.
“We therefore expect the market to fully value this highly attractive business in line with its peers.
“For all of these reasons, we believe that the true value of GKN is over £5 per share and that Melrose’s final offer fundamentally undervalues your company and should be rejected.”
Numis analyst David Larkam said that while the Driveline deal has strategic merits, it is being sold “too cheaply and too early”.
“We see the combination of Dana and GKN Driveline as making industrial and commercial sense as scale benefits increase. Synergy benefits also help to support a transaction.
“Both have electric vehicle capabilities, although we believe GKN is more advanced, as highlighted by current auto programmes,” Mr Larkam said.