The Duchess took a scheduled British Airways flight to the Netherlands where she carried out a day of engagements in The Hague and Rotterdam.
Her first stop was to call on King Willem-Alexander at Villa Eikenhorst, where the monarch lives with his wife Queen Máxima, who was away in Argentina, and the couple's three daughters.
Kate met King Willem-Alexander at his official residence Villa Eikenhorst
Kate, who looked elegant in a Catherine Walker outfit, had a meeting with the king in which he officially welcomed her to the country over lunch.
The Duchess then visited the Mauritshuis museum to view an exhibition, At Home in Holland: Vermeer and his Contemporaries from the British Royal Collection.
The Duchess is carrying out a day of engagements in the Netherlands
The cultural visit will have been particularly interesting for Kate, who studied history of art at university. The exhibition features 22 works by Dutch artists from the 17th century.
Kate toured the gallery's permanent collection before visiting the exhibition. The mum-of-two also met children taking part in the gallery's learning programme, followed by a short reception with museum supporters.
She visited the Mauritshuis museum in The Hague
Kate then visited the British Ambassador's Residence in The Hague where she took part in a roundtable discussion on the themes of addiction, intervention, family and mental health.
The Duchess is a keen campaigner for mental health, especially in young people and children. The discussion brought together professionals from the renowned Trimbos Institute of the Netherlands, and two of Kate's UK charities of which she is patron – the Anna Freud Centre for Children and Families and Action on Addiction.
The Duchess looked elegant in a Catherine Walker outfit
Her last engagement of the day took Kate to the neighbouring city of Rotterdam to visit Bouwkeet, a new community-focused initiative in the centre of an economically deprived district.
Local residents can use the facilities, and 'pay' by sharing their skills with others, providing education and positive role models within the community. The centre also works with local schools to bring young people in the area into workshops, where they learn to design, create and build their own projects.
Tuesday's trip was Kate's first solo official visit abroad after she was unable to travel alone to Malta in 2014 due to morning sickness. At the time Kensington Palace had just announced her second pregnancy.