The Debt Management Office estimates that Britain has paid some £5.5 billion in total interest on the 5% and 3.5% war loans since 1917.
Current low interest rates mean the Government is able to refinance the debt with new bonds.
The Treasury is also looking to remove all six of the other remaining undated gilts in its portfolio, including some debt originally issued in the era of the South Sea Bubble in the 18th century.
The plan to repay the First World War debt was announced in December, when Chancellor George Osborne said: "We can, at last, pay off the debts Britain incurred to fight the First World War.
"It is a sign of our fiscal credibility and it's a good deal for this generation of taxpayers. It's also another fitting way to remember that extraordinary sacrifice of the past."
