The 26-year-old Tunzi was declared the winner at a televised event, hosted by American comic-turned-TV personality Steve Harvey, held at Tyler Perry Studios here on Sunday.
Indian contestant Vartika Singh crashed out of the world's biggest beauty pageant after securing a place in the top 20.
Hailing the power of dreams, Tunzi took to Twitter to express gratitude over her victory.
"Tonight a door was opened and I could not be more grateful to have been the one to have walked through it.
"May every little girl who witnessed this moment forever believe in the power of her dreams and may they see their faces reflected in mine. I am #MissUniverse2019," she wrote on the microblogging site.
Tunzi also shared her picture wearing the crown.
Miss Puerto Rico Madison Anderson was named the first runner-up, followed by Mexican contestant Ashley Alvidrez as the second runner-up. Also part of the top 5 were Colombia and Thailand.
The announcement of the winner was made on Miss Universe's official Instagram account.
Miss Universe 2018 Catriona Gray, from the Philippines, presented Tunzi with the crown.
This is the third Miss Universe crown for South Africa, with Demi-Leigh Nel-Peters being declared the winner in 2017.