The Duchess gave birth to the girl, now the fourth in line to the throne, at St. Mary's Hospital in Paddington, London on Saturday morning (02May15) and after around 12 hours, they stood on the steps of the Lindo Wing to introduce their new arrival.
William smiled and waved as his wife, who wore a yellow and white dress, cradled the sleeping child, who wore a white bonnet and shawl. They returned into the hospital to secure the Princess into a car seat, before heading back outside, where William drove them back to Kensington Palace.
Their son Prince George was waiting for them to return home after visiting the hospital earlier in the day and posing with his father on the steps.
A spokesperson wrote on Twitter.com, "Their Royal Highnesses would like to thank all staff at the hospital for the care and treatment they have all received... They would also like to thank everyone for their warm wishes."
On Sunday (03May15), William's father Charles, Prince of Wales, his wife Camilla, and the Duchess' mother Carol Middleton and sister Pippa were spotted driving into Kensington Palace to visit the baby for the first time, according to Sky News.
The family are expected to relocate to their Anmer Hall mansion on Queen Elizabeth II's Sandringham estate in Norfolk, England in the next few days.