Kate, 42, was admitted on Tuesday for the successful planned procedure, but is expected to stay in the private London Clinic for 10-14 days before returning to her Adelaide Cottage home in Windsor.
She is said to be “doing well” but will spend up to three months away from royal duties.
Caring William was seen visiting Kate Middleton in hospital following her abdominal surgery.
And Kate’s family have also been eager to support her recovery and care.
The Princess of Wales is known to have a strong bond with her parents Carole and Michael Middleton and siblings Pippa Matthews and James Middleton.
The family, who live nearby in Berkshire, will be on hand to support her recovery with Michael and Carole well used to having the children over for sleepovers.
Meanwhile her siblings Pippa Matthews and James Middleton are readying themselves to help support Kate when she returns to her Windsor home.
Doting Prince of Wales, 41, arrived at the London Clinic yesterday afternoon to see his wife as she recovers from the planned procedure.
William was seen driving an Audi e-Tron GT Carbon Vorsprung from the back entrance yesterday, followed by a Land Rover Discovery.
It is understood that William wants to continue doing the school run in an effort to create as much normality as he can for Prince George, ten, Princess Charlotte, eight, and five-year-old Prince Louis, while their mother is in hospital.
He will also take time off and step back from all official duties for several weeks.
A short statement from Kensington Palace said: “The Prince has just left hospital after visiting his wife.”
A statement from the Palace read: “The Princess of Wales appreciates the interest this statement will generate.
“She hopes that the public will understand her desire to maintain as much normality for her children as possible; and her wish that her personal medical information remains private.
“Kensington Palace will, therefore, only provide updates on Her Royal Highness’ progress when there is significant new information to share.
“The Princess of Wales wishes to apologise to all those concerned for the fact that she has to postpone her upcoming engagements.
“She looks forward to reinstating as many as possible, as soon as possible.”
It comes as the King is also preparing for a corrective procedure after being diagnosed with a benign enlarged prostate.
Queen Camilla was seen today after the news was revealed by the Palace – saying her husband the King was “fine” and “looking forward to getting back to work.
Kate’s announcement came just 90 minutes before Buckingham Palace confirmed the King would also receive treatment in an unprecedented double royal health scare.
The 75-year-old monarch, who acceded to the throne 16 months ago, will be admitted to hospital next week.
He was said to be keen to go public with his condition to encourage other men who may be experiencing symptoms to get checked.
The King is staying at Birkhall in Aberdeenshire with the Queen but the Palace has not confirmed whether he will be treated in London or Scotland.
The Queen, who was visiting the Aberdeen Art Gallery, was asked about the King by the Lord Provost.
She replied: “He’s fine, thank you very much. Looking forward to getting back to work.”
Kate is not expected to return to public events until after Easter, and her husband will combine being by his wife’s and children’s side throughout.
Any royal tours William and Kate had in the diary for the coming months will also no longer take place amid speculation they would visit Italy together in March.