Welhaven was a student at the Statens håndverks- og kunstindustriskole (now Norwegian National Academy of Craft and Art Industry) in 1870. He later studied architecture at Technische Hochschule (now Leibniz University Hannover) during 1871-73. He started practicing as an architect from 1875. In 1883 he was appointed manager for the Royal Palace in Oslo by King Oscar II. He was also responsible for Prinsehytta, Skinnarbøl the Bygdøy Royal Estate and Oscarshall. From 1905 he continued in this position for King Haakon VII of Norway, and led the comprehensive modernization project of the Royal Stables between 1905 and 1911, until he finally retired in 1920.[3]
Besides his duties as a palace manager, he continued his architectural work.[3]
Among his designs were the tourist cabins Glitterheim and Gjendebu, and Polhøgda, the home of Fridtjof and Eva Nansen.[4] He also designed several private dwellings in Oslo.[5]