David Oddsson was born on 17 January 1948 in Reykjavik, Iceland, to Oddur Olafsson, a medical doctor, and Ingibjorg Kristin Ludviksdottir, a bank department chief. He was educated in Iceland and graduated from Reykjavik Higher Secondary Grammar School in 1970. He attended the University of Iceland and received a degree in law in 1976.
While attending college, he held several jobs. From 1970 to 1972, he worked as chief clerk at Reykjavik Theatre. Oddsson continues to be a comic playwright in his spare time. He was a parliamentary reporter for Morgunbladid, Iceland's largest newspaper, from 1973 to 1974. He held a position at Almenna bokafelagid (Book Publishers and Book Club) from 1975 to 1976. In 1970, Oddsson married Asgridur Thoracensen, a nurse. Their son, Thorsteinn Davidsson (born 12 November 1971) is a lawyer.
From 1968 to 1975, Oddsson produced several radio programs for the Iceland State Broadcasting Service. He has cowritten two plays and authored three television dramas. His plays have been broadcast in other Nordic countries. He has also written two political books, namely Sjalfstaedisstefnan (The Independence Movement), published in 1981, and Eistland: Smapjod undir oki erlends voids (Estonia, a Small Nation under the Yoke of a Foreign Power), published in 1973. It was under Oddsson's leadership that Iceland became the first country to recognize Estonia's independence in 1991. While serving as prime minister, he has continued to write, publishing two best-selling collections of short stories, A Couple of Days Without Gudny (1997) and Stolen from the Author of the Alphabet (2002). Oddsson also enjoys playing bridge and fishing in his leisure time.