The Queen made the short journey from Buckingham Palace to Prince William and Kate Middleton's home in central London in a dark green Bentley.
A Kensington Palace spokesman said it was "now private and quiet time for them to get to know their son".
The monarch had said she was "thrilled" at the arrival of her third great-grandson during a reception at Buckingham Palace yesterday evening.
The 34-minute visit came ahead of her departure on Friday for Balmoral in Scotland for her traditional summer break.
The Queen was not the first visitor to meet the royal baby prince. The Prince of Wales and Duchess of Cornwall, and Catherine's parents, Carole and Michael Middleton, paid visits to the hospital yesterday afternoon.
Prince Charles visited his first grandchild and the third in line to Britain's throne, accompanied by his wife Camilla Parker-Bowles.
He had triggered a frenzy among the waiting reporters and camerapersons as he said on his departure: "He (royal baby) is marvellous. You will see in a minute".
George is the bookies' favourite for the first name of the prince, who is destined to be king one day. James and Alexander are among other names on a short-list.
Royal fans waited seven days before the name of a newborn Prince William was announced in 1982, and there was a wait of a month following the Prince Charles's birth in 1948.
The third in line to the throne and his parents had emerged from St. Mary's Hospital in Paddington yesterday evening to a flurry of flashbulbs from the swarm of cameras waiting to capture the first glimpse of the royal baby born on Monday .
The baby raised a tiny hand above his white blankets but remained quiet.
Speaking outside the hospital, William said they were "working on a name" and would choose one "as soon as we can".
"He has a good pair of lungs on him and he's quite heavy. We are still working on a name," said William, taking the little prince from his wife's arms.
31-year-old Kate said: "It is a very emotional moment, like any new parent would know".
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