In a statement his family said the 74-year old had been battling a “long illness” for the last month in hospital.
Langa retired from the bench in 2009, and had already been admitted to a hospital in Durban earlier this year.
The Bushbuckridge-born lawyer was appointed as one of the 11 founding judges of the Constitutional Court by then president Nelson Mandela in 1994. He became the deputy chief justice in 2001, and took over the helm of the court in 2005.
In 2008 he was awarded the Order of the Baobab in Gold for his exceptional service to law, constitutional jurisprudence and human rights.
President Jacob Zuma extended his condolences in a statement on Wednesday.
"The country has lost one of its best legal minds, a dedicated Human Rights jurist and a veteran struggle activist. On behalf of government and the people of South Africa, we wish to convey our deepest condolences. May his soul rest in peace," said President Zuma.
After his retirement as chief justice in 2009 he was instrumental in chairing the Press Freedom Commission, which helped draft new regulations for the press in South Africa.
Langa attained his law degrees while studying long-distance through the University of South Africa, while working as an interpreter and messenger at the Department of Justice. He was then admitted as an Advocate of the Supreme Court of South African in June 1977.
In the 1980s he helped found the National Association of Democratic Lawyers, and served as its president until 1994. He was also involved in founding the South African Legal Defence Fund.
He practiced law at the Natal Bar and became a Senior Counsel just before he was appointed to the Constitutional Court in 1994.
Langa was married to Thandekile Langa in 1966 and had six children. She passed away at Milpark Hospital in 2009 after a long battle with Parkinson's disease. According to his biography at the Constitutional Court, he enjoyed walking, jogging, listening to music and reading.