[1]: 19  After high school, he attended Fort Hare University and became active with the African National Congress (ANC).

[1]: 19  In 1986, he was deputy chair of the ANC's constitutional committee with members such as Jack Simons, Kader Asmal and Albie Sachs.

He helped to set up the Centre for Development Studies and the South African Legal Defence Fund, both at the University of the Western Cape.

According to ANC Secretary-General Gwede Mantashe, Skweyiya voluntarily chose to leave parliamentary politics, "contrary to current speculative and surreptitious commentary".

[5] Skweyiya was appointed by President Jacob Zuma as the South African High Commissioner to the United Kingdom in September 2009.

[7][8] Skweyiya died at a Pretoria hospital on 11 April 2018, at the age of 75,[9] leaving behind his second wife, Thuthukile, and two stepchildren, and a son from his first marriage.