Elfsberg grew up in the district of Svedmyra in southern Stockholm. He received his upper-secondary education at Norra Real in Stockholm and then studied at the Department of Journalism, Media and Communication (JMK) at Stockholm University, from where he dropped out to work as a trainee at the daily news program Rapport at Sveriges Television (SVT) in 1971. He presented the program for the first time in 1975 and then worked as a news presenter for over thirty years, eventually earning the nickname "Mr. Rapport". He temporarily left Rapport in 2003 to host the interview program 24 minuter on the SVT channel SVT24. He has also presented the SVT program Dokument utifrån. From January 2005 to December 2007, Elfsberg worked as the "ombudsman of the viewers" (Swedish: tittarombudsman) at SVT. Since April 2008 he will lead the news program Play Rapport on SVT's video on demand service SVT Play.
Elfsberg is currently married to Monica Elfsberg and has three children from two earlier marriages.
- Hagen, Cecilia (2008-01-13). "Det finns saker som jag ångrar" (in Swedish). Expressen. Retrieved 2008-04-01.
- "Elfsberg blir ombudsman för publiken" (in Swedish). Sveriges Television. 2004-11-30. Retrieved 2008-04-01.
- Wijnbladh, Olof (2007-11-13). "Elfsberg slutar som tittarombudsman" (in Swedish). Dagens Nyheter. Retrieved 2008-04-01.
- "Claes Elfsberg leder Play Rapport - SVT:s nya nyhetskanal på webben" (Press release) (in Swedish). Sveriges Television. 2008-01-03. Retrieved 2008-04-01.