Gurirab was born in Usakos in Erongo Region. In exile from 1962 to 1989, he was Associate Representative of the SWAPO Mission to United Nations and United States from 1964 to 1972, then Head of the SWAPO Mission to the United Nations from 1972 to 1986. Subsequently he was SWAPO's Secretary for Foreign Affairs from 1986 to 1990.
He was a SWAPO member of the Constituent Assembly, which was in place from November 1989 to March 1990, immediately prior to independence, and since 1990 he has been a member of the National Assembly. He was Minister of Foreign Affairs from independence in 1990 until he was appointed as Prime Minister by President Sam Nujoma on August 27 2002, replacing Hage Geingob.
He received the sixth highest number of votes—377—in the election to the Central Committee of SWAPO at the party's August 2002 congress. He was again one of the highest scoring candidates in the election to the Central Committee at SWAPO's November 2007 congress.