"The Queen, The Duke of Edinburgh, The Prince of Wales, The Duchess of Cornwall and Prince Harry and members of both families are delighted with the news," a St. James Palace news release said.
Middleton was admitted Monday afternoon to King Edward VII Hospital in Central London with hyperemesis gravidarum, or acute morning sickness.
"As the pregnancy is in its very early stages, Her Royal Highness is expected to stay in hospital for several days and will require a period of rest thereafter," the release said.
The couple was married April 29, 2011. Both Will and Kate are 30.
In recent days, Middleton has kept up royal appearances - recently playing field hockey with schoolchildren at her former school.
The confirmation of her pregnancy - following intense speculation ever since their lavish Westminster Abbey wedding last year - was greeted with congratulations.
Prime Minister David Cameron wrote on Twitter that he was "delighted by the news," saying the royals "will make wonderful parents."
Not only are the attractive young couple popular - with William's easy common touch reminding many of his mother, the late Princess Diana - but their child is expected to play an important role in British national life for decades to come.
As the first-born to William - who is second in line for the throne after his father, Prince Charles - the couple's child stands an excellent chance of one day becoming monarch.
Whether boy or girl, the child will be next in line behind William in the line of succession to the throne, Cabinet Office officials have said.
Leaders of Britain and the 15 former colonies that have the monarch as their head of state agreed in 2011 to new rules which give females equal status with males in the order of succession.
Although none of the nations had legislated to make the change as of September 2012, the British Cabinet Office confirmed that this is now the de-facto rule.
"It's not unusual for pregnant women to get morning sickness, but when it gets to the point where you're dehydrated, losing weight or vomiting so much you begin to build up (toxic) products in your blood, that's a concern," said Dr. Kecia Gaither, director of maternal fetal medicine at Brookdale University and Medical Center in New York.
"As for the pregnancy, it doesn't pose a threat to the baby, just for the mom- maintaining her weight and hydration," said Dr. Alicia Mandujano, Advocate Illinois Masonic Medical Center.
The condition is thought to affect about one in 50 pregnant women and tends to be more common in young women, women who are pregnant for the first time, those expecting multiple babies and in non-smokers. Gaither said that fewer than one percent of women with the condition need to be hospitalized.
Doctors aren't sure what causes it but suspect it could be linked to hormonal changes or nutritional problems.
Women admitted to the hospital with hyperemesis gravidarum are usually treated with nutritional supplements and given fluids intravenously to treat dehydration. Dr. Dagni Rajasingam, a spokeswoman for the Royal College of Obstetricians and Gynaecologists, said most women hospitalized with the condition are discharged within several days.
"It depends on how well the woman is keeping fluids down," she said.
If the problem is recognized and treated early, doctors say there are no long-term effects for either the mother or the child. Left untreated, the mother could be at risk of developing neurological problems - including seizures - or risk delivering the baby early.
Gaither said the condition usually subsides by the second trimester.
"The rest of the pregnancy could be entirely uneventful," she said, adding that pregnant women treated for the condition are usually advised to avoid fatty foods that could aggravate the problem.
Gaither said the duchess would probably be able to meet her usual royal obligations by her second trimester.
"She should be able to meet all her public obligations soon," she said, advising her to take her vitamins and ensure there are no other underlying health problems. "She should just be looking forward to having a healthy little plump person."
The Associated Press contributed to this report.