Todorčević was born at Ubovića Brdo, Bosnia and Herzegovina where he lived until the second grade of primary school. After, his family moved to Banatsko Novo Selo where he finished primary school. He enrolled "Uroš Predić" grammar school in Pančevo. He demonstrated his talent and affinity toward mathematics in the third and fourth years of the grammar school. After finishing grammar school he enrolled Faculty of Science, Belgrade University, where he studied pure mathematics. During his undergraduate studies he attended Đuro Kurepa's advanced mathematical classes. In 1978 he finished graduate studies. Kurepa validated Todorčević's master thesis as good enough to be accepted as a doctoral thesis. Regardless, Todorčević wrote his doctoral thesis in 1979 with Kurepa as his advisory. In his address, preceding the oral defense of the doctoral thesis, Kurepa stressed that he was not able to find external readers of the Stevo's doctoral thesis in Yugoslavia, capable of fully understanding and evaluating Stevo's work, and turned to two university professors from England. Kurepa added that Stevo's talent was a miracle and that Stevo was the most talented out of the 40 Ph.D. students he advised in the past.