Kristian completed his apprenticeship as cabinetmaker in 1942. From 1944-45 he was visiting student under professor Kaare Klint at the Department of Furniture at the Royal Academy of Fine Arts in Copenhagen. In 1946, he graduated from the Furniture Design Department of the School of Arts, Crafts and Design in Copenhagen, where he also lectured 1953-56. He served as chairman of Danish Furniture Designers 1947-49. He was instrumental in establishing the Industrial Designers of Denmark and served as the society's first chairman, from 1966 to 1968.
Between 1968 and 1971,Vedel organised and led the Department of Industrial Design at the University of Nairobi, Kenya. He and his wife, Ane, returned
to Denmark in 1972 to establish a design studio on Thyholm, in North-Western Jutland. Influenced by Kaare Klint and the German Bauhaus school,
his "classic modern" designs are characterized by creative use of materials, especially plastics and wood.
In an interview, Kristian Vedel stated his position as follows:
The starting point for an industrial artist's work must always be that he, from his own point of view, and as objectively as possible, takes a position with regard to what he feels society and his fellow men need; he must personally take a stand on the existing possibilities and responsibilities.
Vedel was awarded 1st prize by Copenhagen Cabinetmakers Guild (1947), Louisiana Museum Prize (1957), silver medal at La Triennale di Milano for children's furniture (1957), a gold medal at La Triennale di Milano for his line of stackable melamine dishes and containers, the Design Award at Interplast in London (1961) and the Lunning Prize (1962).
In January-May 2007, Trapholt Museum in Denmark mounted a retrospective exhibition of major works. As an adjunct to the exhibition,