The US delivery firm has made an all-cash offer of €8.00 per share for the Dutch delivery group, valuing TNT at €4.4bn (£3.2bn).
The offer represents a 33 per cent premium on its previous closing price.
A major shareholder, PostNL which holds a 14.7 per cent stake in the company, will back the deal, which is expected to close in the first half of the 2016.
FedEx said it plans to divest TNT's airline operations and the combined operations will be located in Amsterdam and Hoofddorp, with TNT's existing operations in Liege to continue.
Frederick Smith, FedEx boss, said: "We believe that this strategic acquisition will add significant value for FedEx shareowners, team members and customers around the globe. This transaction allows us to quickly broaden our portfolio of international transportation solutions to take advantage of market trends - especially the continuing growth of global e-commerce - and positions FedEx for greater long-term profitable growth.”
TNT chief executive Tex Gunning said the company had not solicited a deal, but that the bid is "good news for stakeholders".
"Our people and customers can profit from the true global reach and expanded propositions, while with this offer our shareholders can already reap benefits today that otherwise would only have been available in the longer run," said Gunning.