The grey hat, size 6 and 7/8, with the initials WSC stamped in the silk lining, was a present from Churchill to Harry Hopkins, a special adviser to President Roosevelt during the Second World War.
Mr Hopkins, who was bald and suffered ill-health, was a frequent visitor to London and had many discussions with Churchill, the Prime Minister who was trying to persuade the Americans to enter the war.
On one such occasion as they were preparing to go out, Churchill, who was rarely seen without a hat, noticed the cold weather and offered one of his own hats to his friend to cover his bare head. Mr Hopkins was delighted and was often seen wearing the hat until his death in 1946.
Alan Kucia, the senior archivist at the Churchill Archive in Cambridge, said Mr Hopkins worked very closely with Sir Winston and the two were in regular contact.
"Churchill was a great collector of hats and he was very generous so it would not surprise me that he would have given one to his friend," he said.
"Hopkins died right after the war and we have several telegrams from Churchill to him asking about his health. They were friends as well as working together and Hopkins was entertained at Chequers."
Nicholas Soames, MP and grandson of Sir Winston, said: "Harry Hopkins was a great friend of his and he gave him the hat as a mark of affection.
"I am sure he would have worn it - he wouldn't have given him a hat he didn't wear."
Churchill memorabilia remains extremely popular and last year one of his top hats fetched pounds 22,000 when it was sold in London.
The homburg, to be sold in New York, was originally discovered when Mr Hopkins' widow called in an antique dealer to clear her attic. The dealer felt the hat should be returned to the British and took it to the British Information Service in New York and it was presented to D'Arcy Edmonson, who was head of the office at the time.
Mr Edmonson was greatly looking forward to wearing the hat and was apparently distressed to find it would not fit. But the hat was a perfect fit for his colleague Charlie Campbell, a senior press officer at the British Embassy, who also enjoyed wearing it.
His widow, Dorothy, who is selling the hat, said her husband was a great admirer of Sir Winston. "Charlie used to accompany Churchill on his visits to Washington during the war and he really admired him," she said. "He was so happy when the hat fitted him and he used to wear the hat to the office and to walk our dog, Mr Cholmondley.
"Charlie died suddenly in 1956 and I have been carrying the hat around with me since, but now I have decided that I really don't need it any more and I am going to sell it."