William arrived at the King Edward VII private hospital just before noon.
Royal officials announced Monday that Kate is pregnant and suffering from hyperemesis gravidarum, a severe form of morning sickness that can lead to dehydration or worse if left untreated. She is expected to remain hospitalized for several days.
The pregnancy comes after a 2011 decision by the leaders of Britain and 15 Commonwealth nations endorsing new rules that give girls equal status with boys in the order of succession.
Experts caution that laws to enact the change have not yet been passed, which could cause uncertainty if the baby is a girl.