Kate placed a hand on his back during the greetings with senior staff and when the royals first arrived, Eton's headmaster Simon Henderson told the future king: "Welcome, good luck, enjoy it."
The prince and princess travelled with George the short distance from their home in Forest Lodge, Windsor Great Park, to the renowned private school, which has educated a string of prime ministers and Hollywood stars.
Later on Wednesday, Kensington Palace released photos of George on Instagram, wearing Eton's formal uniform of a black tailcoat, waistcoat, pin-striped trousers and stiff, white peter pan collar.
The young prince is following in the footsteps of father William and Uncle Harry, who both attended the college, located just across the River Thames from Windsor Castle in the town of Eton.
George and his parents arrived in School Yard, the Berkshire institution's historic quadrangle overlooked by Lupton's Tower, a Tudor landmark, and at its centre was a statue of King Henry VI, who founded Eton in 1440.
Heavy rain had been falling all morning and only Kate sheltered under an umbrella as they walked across the square towards Eton's head master and the provost, Sir Nicholas Coleridge. William carried a folded umbrella, and George stood between his parents.
The group chatted for a few moments and Henderson was overheard telling George: "Welcome, good luck, enjoy it."
When one of the party mentioned the rain, the provost, whose role is similar to a school's chair of governors, replied "typical" and William added to laughter: "If it rains, it rains for ages."
They then walked through a doorway into one of the oldest parts of Eton and Kate was seen to put her hand on her son's back.
Beyond academic learning and sporting activities, Eton has a reputation for instilling self-reliance and leadership as students have to fulfil many non-academic tasks themselves.
Admission is rigorous, with the boys going through stringent tests and parents pay an annual fee of £63,298 ($A118,738) for a school whose name is likely to be more influential than the academic qualifications gained by pupils.
William was an Eton pupil for five years beginning in 1995 and served as a house captain and prefect before leaving to study at St Andrews University, while Harry joined three years after his brother.
Eton's roll call of famous past students includes actors Tom Hiddleston, Hugh Laurie and Eddie Redmayne, a large number of prime ministers including Lord David Cameron, writers George Orwell and Ian Fleming, and adventurer Bear Grylls.
George turned 13 in July and has spent part of the summer in Scotland with his family enjoying a break from studies after leaving Lambrook School, a private prep school in Berkshire he attended with siblings Princess Charlotte, 11, and eight-year-old Prince Louis.
The prince will have to get used to his new life at Eton over the coming weeks, where pupils call teachers beaks and live in one of 25 boarding houses led by a house master and dame providing pastoral care and support.
George arrived wearing smart casual clothes - dark trousers, a jacket, shirt and tie - and later changed into "school dress", a uniform standardised in the 1960s of a black tailcoat, waistcoat and pinstriped trousers, with a stiff white collar.
William and Harry were allowed to complete their time at Eton without media intrusion and William and Kate will be hoping George receives the same courtesy.
Other new intakes arrived later in the morning after the prince and his parents, and some will have brought their possessions in traditional boarding school trunks.
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