The Duke and Duchess of Cambridge are expecting their baby in April.
Kensington Palace said William and Kate were "delighted" to confirm the month their third child is due to be born.
Kate has been suffering from hyperemesis gravidarum - a severe form of morning sickness - but made a surprise appearance at a royal engagement on Monday, and is due to visit Norway and Sweden with the Duke on an official visit early in 2018.
The new royal baby should arrive the month before the Cambridges' daughter Princess Charlotte turns three.
But Kate is believed to have gone beyond her due date with both Prince George and his sister.
The Duchess gave birth to George and Charlotte at the private Lindo Wing at St Mary's Hospital in Paddington, central London, and will be expected to do the same, unless she opts for a home birth.
The new baby will be born fifth in line to the throne, pushing uncle Prince Harry into sixth place.
It is likely Kate has now had her 12 week scan and seen an ultrasound image of her baby.
Soon after the news of the pregnancy was revealed in September, William revealed there was "not much sleep" being had at the main family home of Kensington Palace as Kate fought her severe morning sickness.
"We need Catherine to get over this first bit and then we can start celebrating," he said at the time.
"It's always a bit anxious to start with, but she's well."
The official visit to Norway and Sweden was originally scheduled for next month, but has been delayed because of Kate's sickness.
William is going ahead with a solo trip to Finland in November, being committed to the schedule in order to mark the centenary of the country's independence in 2017.
Depending on the exact date of the joint tour, Kate could be heavily pregnant when she makes the trip with William to Norway and Sweden in the depths of the Scandinavian winter.
She made a surprise appearance at a royal engagement on Monday when she took a twirl with Paddington Bear as they danced on the platform of Paddington Station, watched by William and Harry, at a charity event.
With the Duchess believed to be just over 12 weeks pregnant, it is likely the baby is due around the end of April.
The prince or princess could possibly arrive on William and Kate's seventh wedding anniversary on April 29 or close to Princess Charlotte's third birthday on May 2.
It is thought Charlotte's birth was overdue but if the Duke and Duchess' third child is born early it could coincide with the 92nd birthday of its great-grandmother the Queen on April 21.