Kate, who is expecting her third child, will be well into her pregnancy when she makes the trip early in 2018.
Kensington Palace said the couple had been asked to undertake the Scandinavian visit on behalf of the Foreign Office.
The royal household also announced that William is to make a solo official visit to Finland next month.
He will travel to the country, without Kate, on Wednesday November 29 and Thursday 30, also at the request of the Foreign Office.
The Duchess is suffering from hyperemesis gravidarum - a severe form of morning sickness - but made a surprise appearance at a royal engagement on Monday.
She took a twirl with Paddington Bear as they danced on the platform of Paddington Station, watched by William and Prince Harry, at a charity event.