In a joint statement, FedEx and TNT said both management boards had reached a “conditional agreement”.
FedEx has offered shareholders €8 per share, a 33% premium on TNT’s closing share price on April 2.
It comes two years after United Parcel Service (UPS) pulled out of a €5.2 billion bid for the Dutch firm.
UPS pulled out of the deal following opposition from EU competition authorities, saying it saw “no realistic prospect” of approval for its bid from the European Commission.
Since then TNT has undertaken a restructuring program, cutting costs, selling operations and investing heavily in its road network to hold on to customers in what has been a weak European market for business package deliveries.
FedEx and TNT Express expect the deal to be completed in the first half of 2016 and say they are confident any European competition concerns can be overcome this time.
The European regional headquarters of the combined companies will remain in the Netherlands, while FedEx has promised to maintain the TNT Express brand “for an appropriate period”.
TNT Express CEO Tex Gunning said: “This offer comes at a time of important transformations within TNT Express and we were fully geared to executing our stand-alone strategy.
“But while we did not solicit an acquisition, we truly believe that FedEx’s proposal, both from a financial and a non-financial view, is good news for all stakeholders.”
However, the terms of the takeover allow for a competitor to make an offer within the next eight weeks and for the current deal to be terminated if that offer exceeds the existing proposal by 8%.
TNT Express warned in February 2015 that it expected adverse trading conditions to continue in its main western European markets this year, as it reported a €196 million annual loss on revenues which fell 3.2% to €6.6 billion.
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