She met the country's Princess Stephanie and Prime Minister Xavier Bettel at the capital city's museum of modern art, Mudamon.
The Duchess was given a guided tour of the exhibitions by British artists Sir Tony Cragg and Darren Almond.
The treaty, signed in 1867, confirmed Luxembourg's independence and neutrality.
On the trip Kate, who is a patron of the National Portrait Gallery, met people who worked in the arts and charitable sectors in Luxembourg.
She also spoke to Oscar-winning director Laurent Witz, who won an academy award in 2014 for the Best Animated Short Film, Mr Hublot.
Before leaving Luxembourg she was introduced to schoolchildren, aged five and six, from St George's International School.
The UK's deputy ambassador to Luxembourg said: "We have a good strong bilateral relationship and always have with the Luxembourgers, they still very much recognise the role we had in liberating them during the war and we have a very strong relationship between the two financial centres particularly, and that's something we are very anxious to continue and maintain.
"There are also close ties between the two royal families, with three generations of the Luxembourg royal family having been educated at our military academy at Sandhurst."
The Duchess of Cambridge has visited Luxembourg on her second solo trip, to mark 150 years of the Treaty of London.