Kate, 42, was admitted to The London Clinic on Tuesday for the planned procedure.
A spokesman on Wednesday said the surgery at the London Clinic was successful and the princess is expected to remain in hospital for 10 to 14 days, before returning home to continue her recovery.
Palace sources told the Times she is “doing well” as she recovers in hospital.
The announcement came shortly before it was revealed the King will attend hospital next week for treatment for an enlarged prostate. His public engagements will also be postponed for a short period while he recovers.
The recovery period required after Kate's surgery means all her scheduled engagements will be postponed until after Easter, which falls on March 31.Heir to the throne William will combine being at Kate's side with caring for their children Prince George, Princess Charlotte and Prince Louis, and he has postponed a number of engagements.There will now be no international travel for the prince and princess in the coming months.
The Palace refused to confirm what Kate was being treated for but confirmed the condition was non-cancerous.
Kate is close to her family, and her parents Carole and Michael Middleton and siblings Pippa Matthews and James Middleton are set to rally round and help support her recovery at the Waleses' home in Windsor.
The Kensington Palace spokesman said: “Based on the current medical advice, she is unlikely to return to public duties until after Easter.
“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.”
The princess had a full calendar of public engagements in December, and was last seen in public at the Royal Family's Christmas Day service in Sandringham.
Reporters and TV camera crews gathered outside the London Clinic on Wednesday afternoon, after news of Kate's admission broke. Police officers were also seen outside the building.
The London Clinic is near Regent's Park and is said to be the UK's largest independent private hospital.
The princess marked her 42nd birthday just over a week ago, with the monarchy’s official social media accounts sharing a new behind-the-scenes photo of the princess at the King’s coronation.
Kate usually enjoys good health but was previously admitted to hospital while pregnant after suffering from hyperemesis gravidarum – severe morning sickness.
Like the rest of the royal family, she has had a busy, turbulent past couple of years, with the Platinum Jubilee and the late Queen’s death in 2022, and the coronation in 2023, as well as adjusting to her new role as the Princess of Wales.
A statement from Kensington Palace pic.twitter.com/6h3BCrqj5L
— The Prince and Princess of Wales (@KensingtonRoyal) January 17, 2024
The Waleses also faced the ongoing rift between William and his brother the Duke of Sussex, with Harry making controversial claims about Charles, Camilla, William and Kate in his Netflix documentary and memoir Spare.
The princess has thrown herself into charity work since her marriage to Prince William in 2011, focusing on mental health and early childhood.
Jamie Lowther-Pinkerton, who was private secretary to the Cambridges and the Duke of Sussex, and used to work for the Queen Mother, previously told The Times: “She takes time to talk to people. She is tough.
“She has got that Queen Mother feel in her, so that when things need doing, she is there to do them.”
This story is being updated...