Salome Þorkelsdóttir was born on 3 July 1927, in Reykjavík, Iceland to Þorkell Sigurðsson and Anna Þorbjörg Sigurðardóttir.
In 1947, she married Jóel Kristinn Jóelsson (2 January 1921–16 June 2007) and subsequently, they had three children.
[2] After raising her children, Salome served on the council of the Mosfellshrepps (Moss District) from 1966-1982.
She was elected to the Alþingi as a Member of Parliament representing Reyknesinga in 1979 and served until 1983, when she was re-elected as an Independence Party candidate.
[2] During her time as speaker, she oversaw discussions concerning the formalization of the European Union in 1993 as well as the reorganization and procedural realignments of the Alþingi.