In a joint statement, the companies told the BBC that both management boards had reached a “conditional agreement”.
FedEx has offered shareholders €8 per share, a 33 per cent premium on TNT’s closing share price on 2 April.
It comes two years after United Parcel Service (UPS) pulled out of a €5.2bn 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 programme, 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.
