"I have three Twenty20 tournaments before the World Cup to prove myself and if all goes well, I will have an outstanding chance to take over then as well," Botha said.
"I am looking forward very much to the challenge. It's a huge privilege to take over from Graeme," he was quoted as saying by Afrikaans daily Beeld.
The 28-year-old Botha was named Twenty20 captain after Smith stepped down last week. Smith had said he would also quit ODI captaincy after the World Cup.
All-rounder Botha stood in for an injured Smith in the ODI series in Australia last year and the Proteas notched up a historic win.
"We were successful then and I am going to do my best to repeat that," Botha said, adding that he had enjoyed standing in for Smith.
Although Botha has led the Proteas in eight ODI and five Twenty20 Internationals, he has had to fight for a place in the team for the last two seasons after he twice came under the scanner for bowling with suspect action. He was banned from bowling his 'doosra' by the ICC last year.