One witness said the Foreign Secretary punched the air in delight when he emerged from Tunbridge Wells register office just after 8.30am and found no photographers waiting outside.
The couple, who had been frequently in the headlines since Mr Cook left his wife of 28 years for Ms Regan last August, announced last month that they were to marry at Chevening on 19 April.
However, in a statement released after yesterday's ceremony, they said they had held it sooner "because they wished it to be a private event free from media intrusion".
The timing of the event could not have been better. With the Northern Ireland peace talks nearing a climax and Parliament closed for the Easter recess, publicity about the event was kept to a minimum.
There were also rumours that Mr Cook had pulled off a further victory over his ex-wife Margaret, from whom he was divorced last month. A newspaper report yesterday claimed she was about to publish a book about a political marriage and that its serialisation in a newspaper - believed to be the Sunday Times - was to be announced just before 19 April.
Yesterday Dr Cook was at work at St John's Hospital in Edinburgh. She said she did not want to comment on the marriage, "but I suppose I wish them well".
The Foreign Office statement said: "The couple will be holding a celebration for family and close friends. They will have a honeymoon over the Easter recess before Mr Cook goes back to his desk as Foreign Secretary at this busy time for Britain's foreign policy," the statement went on.Reuse content