Kensington Palace announced the visit on Tuesday, and said the royals would be visiting in "early 2018" at the request of the British Foreign Office.
"This is something exciting for Great Britain and Sweden's relationship. We're looking forward to it!" the British Ambassador to Sweden, David Cairns, wrote on Twitter.
Aidan Liddle, deputy head of mission at Stockholm's British Embassy, also said the news was "exciting".
The exact date is yet to be decided, according to Margareta Thorgren, the head of press at Sweden's Royal Court, who confirmed the official visit.
Speaking to Aftonbladet, Thorgren said that the British royals would meet the Swedish King, Queen, Crown Princess Victoria and her husband Prince Daniel, but that beyond that the details of the trip had not been planned.
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The British Embassy in Oslo also tweeted: "We are delighted that The Duke & Duchess of Cambridge will visit Norway soon. This will highlight the importance of the UK-Norway relationship."
We are delighted that The Duke&Duchess of Cambridge will visit Norway soon.This will highlight the importance of the UK-Norway relationship. https://t.co/P30prFgrim— British Embassy Oslo (@UKinNorway) October 17, 2017
The news followed an early announcement about a trip by William to Finland, which is planned for late November this year. The pregnant Duchess of Cambridge will not be accompanying him on that visit, as she is suffering from acute morning sickness.