The delighted monarch - who has long been synonymous with the breed - has been kept entertained by the dogs while the Duke of Edinburgh is in hospital, The Sun newspaper reported.
The monarch has been without corgis at her side for more than two years after her final one Whisper, died in October 2018.
At the end of last year, the Queen was left with only one pet dog, a corgi-dachshund cross called Candy, when Vulcan – her other dog of the same “dorgi” breed – died.
An insider told The Sun of the new puppies: "Both are said to be bringing in a lot of noise and energy into the castle while Philip is in hospital."
It was thought the Queen had called time on welcoming any more puppies of the breed.
American horse trainer Monty Roberts, who is a personal friend of the monarch, told Vanity Fair magazine in 2012 he had offered to find one to replace a pet that died.
But he said: "She didn’t want to have any more young dogs. She didn’t want to leave any young dog behind. She wanted to put an end to it."
Buckingham Palace declined to comment - it is not known what the puppies are called or their gender.
The Queen and her corgis:
The Queen has been devoted to corgis throughout her life. She has owned more than 30, as well as dorgis, black Labradors and cocker spaniels.
Her first corgi, Susan, was given to her as an 18th birthday present by her parents in 1944.
The Queen had fallen in love with her father’s dog Dookie, a Pembrokeshire corgi, and wanted one of her own.
Susan became the founder of the Queen’s royal dog dynasty, and was even taken on honeymoon by Princess Elizabeth.
The Queen looks after her own dogs as much as possible.
During weekends at Windsor, the corgis would go too and lived in her private apartments.
Over the years, she would feed them herself, whenever her busy schedule permitted.
In 2012, the Queen’s remaining corgis had a starring role in the James Bond sketch the Queen recorded for the London Olympics opening ceremony.
Monty, Willow and Holly greeted the secret agent, played by Daniel Craig, as he arrived at the Palace to accept a mission from the Queen.
Monty, who was 13, died a couple of months later.
Holly was put down in October 2016 after suffering from an illness, leaving Willow as the Queen’s final corgi descended from Susan, but Willow died in April 2018.