Madlanga replaces Justice Zak Yacoob, who retired earlier this year.
In a press release on Monday, President Jacob Zuma congratulated Madlanga "on this appointment and wish him all the best in this new role of promoting constitutional justice in our country. We also acknowledge and thank all the highly capably candidates who were shortlisted for this position."
Madlanga is currently an evidence leader at the Farlam commission of inquiry, which is investigating the deaths of 44 people during wage-related protests in Marikana, North West.
He was also the evidence leader in the inquiry into former national police commissioner Bheki Cele's fitness to hold office.
Madlanga has BJuris degree from the University of Transkei, where he was awarded the Juta prize for best law student in 1981. He also holds an LLB degree from Rhodes University and an LLM from Notre Dame University in the United States.
Madlanga worked as a law lecturer at the University of Transkei and worked as a high court judge, while also acting in the Supreme Court of Appeal, the Constitutional Court and as judge president of the Transkei division of the high court.
He also represented South Africa at the International Court of Justice at the Hague, Netherlands, on behalf of the Republic of South Africa in the matter of the "separation wall constructed by the Israel on Occupied Palestinian Territory".
The appointment would take effect from August 1.