Kate is spending the day in The Hague and Rotterdam, where her itinerary covers a range of events from a visit to an art exhibition of Old Masters to a round-table discussion on a variety of themes from addiction to mental health.
The one-day trip is a royal milestone for the Duchess as she will be travelling abroad by herself without the Duke.
A tour of Malta in 2014 was scheduled to be Kate's first solo trip but she had to cancel as she was suffering from acute morning sickness while pregnant with Princess Charlotte.
Kate will meet King Willem-Alexander at Villa Eikenhorst, the royal residence he shares with wife Queen Maxima and their three daughters, Princesses Amalia, Alexia and Ariane.
The family home is on the forested De Horsten estate in Wassenaar, near The Hague, and, despite being a private residence, the Dutch monarch sometimes hosts foreign guests.
Art is an interest of the Duchess, who is patron of the National Portrait Gallery, and she will visit the Mauritshuis art museum in The Hague to see an exhibition featuring Dutch Old Masters loaned by the Royal Collection, with artwork, furniture and other objects accumulated over centuries by the British monarchy.
The highlight will be Vermeer's The Music Lesson, which Kate will see after touring the gallery's permanent collection.
Before leaving, the Duchess will meet children taking part in the gallery's learning programme and attend a short reception with museum supporters.
At the official residence of Sir Geoffrey Adams, Britain's Ambassador to the Netherlands, Kate will convene a round-table discussion on the themes of addiction, intervention, family and mental health.
Taking part will be professionals from the Trimbos Institute, a non-profit research centre working on the issues of mental health and addiction.
They will be joined by counterparts from two of the Duchess's UK charities - the Anna Freud Centre for Children and Families, a leading charity in the research, teaching and the provision of care for children and young people with mental health issues, and Action on Addiction.
Later Kate will travel to the neighbouring city of Rotterdam to learn about a community initiative that provides a public workshop in an economically deprived district, with facilities aimed at teenagers.
Residents pay by sharing their skills with others, providing education, skills and positive role models in the neighbourhood.
Kate Middleton: Top Holiday Destinations
Kate Middleton: Top Holiday Destinations
Where: Mustique When: August, 2008 The holiday: Kate and William spent a week at this upmarket Caribbean paradise haven, which enjoys year-round temperatures of 80F. The island became well known for being a popular holiday hotspot for Princess Margaret, and is also a favourite with Mick Jagger, David Bowie, and Elton John.
Where: Klosters, Switzerland When: March, 2008 The holiday: Kate and William enjoyed a family getaway when they headed to this exclusive ski resort with Wills' dad Prince Charles. The couple are both a dab-hand at working the slopes, and Kate even showed her cheeky side when she poked William with her ski pole. The royal couple also enjoyed a holiday here in March 2005.
Where: St Andrews, Scotland When: February, 2011 The holiday: OK, it was work mixed with pleasure, but Kate Middleton and Prince William returned to the university where they first met for their second royal engagement in February. Although they were officially there for work, the royal couple were also said to have enjoyed the beautiful local countryside, which prides itself in being part of the Green Tourism Scheme.
Where: Lake District, England The holiday: Kate showed off her inherent sporty side on a family holiday in the Lake District when she was just four years old. The princess-to-be can be seen getting her hands dirty as she climbed rocks with a look of pure joy on her face. Cute.
Where: Johannesburg, South Africa When: November, 2006 The holiday: Kate headed to Johannesburg to celebrate the 21st birthday of Richard Branson's son, Sam. The birthday group reportedly headed off on safari, and, unsurprisingly, travelled first class on Virgin Atlantic.
Where: Ibiza When: September 2006 The holiday: Kate showed off her amazing bikini body when the royal couple enjoyed some sun, sand and sea action in Ibiza in 2006, where they were spotted soaking up the sun on a luxury yacht.
Where: Courchevel, France When: March 2010 The holiday: Ski fanatics Kate and William enjoyed the powder at France's celebrity-favourite resort, Courchevel, in 2010. The pair, who were on holiday with friends and family, including Kate's sister Pippa, were spotted enjoying a 'loving' meal at a moutain-top restaurant.
Where: Kenya, Africa When: November 2010 The holiday: Want to know where Prince William popped the question? The couple were on a luxurious safari holiday in Kenya, where they stayed at the stunning Cheli & Peacock's Lewa Safari Camp situated in the Lewa Conservancy. The camp has 12 sumptuous tents, which cone with ensuite bathrooms, and a swimming pool overlooking the plains. Very romantic.
Where: Birkhall, Scotland When: December 2009 The holiday: Where do you go if you're dating a royal a fancy a weekend of hunting? Your father-in-law-to-be's fabulous country retreat in Scotland, of course. The royal couple spent New Year here in 2009, and regularly enjoy weekend visits to this beautiful hideaway.
Where: Jordan When: 1984 The holiday: It was a pretty long holiday... well, two and a half years to be precise! Kate's family moved to Jordan when she was two, and they lived there until she was four and a half. Kate even attended nursery in Amman. Aww.