Thirty people were rescued from the blaze on the London Duck Tours craft in September, with some passengers jumping into the Thames.
The Maritime and Coastguard Agency says two vehicles are to be granted a safety certificate to allow them to work for an initial three months.
The company said it was looking forward to getting back in the water.
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The DUKW, also known as a Duck, is a six-wheel-drive amphibious truck first made in the US in the mid-1940s, 21,000 DUKWs were produced for use during World War Two to move men and materials ashore where no port facilities existedMany served on D-Day and in the Normandy landings, where 40% of supplies landed on the beaches were carried by DUKWsDUKWs remained in service with the British and other armies into the 1970sSource: The Yellow Duckmarine
The fire in London, which happened near the Houses of Parliament, followed the sinking of a similar vessel in Liverpool, on 15 June.All 31 passengers and two crewmen were safely recovered from the water, with no serious injuries.
Life jacketsA Marine Accident Investigation Branch report blamed both incidents on problems with the vessels' buoyancy foam.
It recommended tourist vessels of this kind, known as DUKWs, should not operate until the problem was resolved.
A Maritime and Coastguard Agency (MCA) spokesman said: "The operator has been working to demonstrate to the MCA that two of its vessels have been improved sufficiently to meet our safety requirements.
"We believe that we should shortly be in a position to issue a short-term certificate to allow them to operate for a period of three months."
On its website, London Duck Tours said: "We'd like to thank all our customers for their support over the past few months and are really looking forward to getting back on the river."
A London Assembly report recommended all passengers on amphibious landing craft used for tourist sailings should wear life jackets.