Broad left the field when the problem flared up on his left heel after bowling just one over for his county Nottinghamshire against Leicestershire last month, putting his participation in the first test in doubt.
The 31-year-old spent two weeks on the sidelines before returning to play in his county's Royal London One-Day Cup final win over Surrey at the weekend.
He failed to take a wicket but sent down nine overs in a boost for England, who are without injured pace duo Chris Woakes and Jake Ball for the opening test of the four-match series.
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"I got through the Lord's final here on Saturday without any problems and I actually bowled on the Wednesday and Friday before that with no pain as well," Broad told Sky Sports.
"It's pulled up really well. We are training this (Tuesday) afternoon and tomorrow and I am really confident.
"I've been playing county cricket since early April so I've had quite a lot of red-ball cricket, so I am not concerned about the workload and it was great to have the intensity of the Lord's final to put the body to the test."
Root will end his long wait to lead the side out on Thursday, nearly four months after he was appointed England's test skipper and replaced his long-serving predecessor Alastair Cook.
"Joe is an attacking cricketer and aggressive when he plays, so I think the team will take that sort of shape," Broad said.
"I don't think he has captained me in a tour game or anything, so I am excited for him and I am sure he is looking forward to getting going.
"He was announced what seems a long time ago and now he gets his opportunity to put things into place, and what a series to be able to do that.
"South Africa have a really good record in England and are a very dangerous team... I think it will be an exciting series to watch."
(Writing by Sudipto Ganguly in Mumbai; Editing by John O'Brien)
