The prime minister, overheard by waiting camera crews while in conversation with ex-New York Mayor Michael Bloomberg, said he had “never heard someone so happy” at the result.
Buckingham Palace declined to comment on Mr Cameron’s remarks.
In the referendum, voters in Scotland rejected independence by 55% to 45%.
Mr Cameron, whose Conservative Party campaigned for such an outcome, discussed the matter with Mr Bloomberg as he walked around the Bloomberg building in New York.
Recalling that he had called the Queen to say “it’s all right”, he said: “She purred down the line. I’ve never heard someone so happy.”