Botha, who underwent the operation on Thursday afternoon, admitted he was hopeful of making a return to international rugby before the November tour to England, Ireland and France.
"The operation went well and it was necessary to do," Botha said.
"I have been struggling for nine weeks now since the Super 14 and we eventually decided that it would be better to sort it out once and for all."
Botha revealed he was initially upset at not being part of this year's Tri-Nations series, but believes the operation would give him a better opportunity of performing at his peak in next year's World Cup in France.
"My heart is still with the team, even though I'm back here and I hope they do well. I just had to look at what was best for my career," he added.
Botha was replaced by Johan Muller for the tournament, but his injury is a huge blow for the Springboks as he and fellow lock Victor Matfield are widely regarded as the best second row combination in world rugby at the moment.