Stubbs, who turns 24 next week, has forged a reputation for his swashbuckling and powerful batting in the Twenty20 format but is now set for a role of some responsibility in the test side.
He has played only one test previously, against India in January where he scored four runs in his two innings and saw South Africa lose by seven wickets.
South Africa have struggled to find a consistent number three in their batting line-up in recent years.
“Tristan’s going to be given a good run in that position,” Conrad said.
“I think his psyche and technique speaks to someone who will do that job really well. And I'm going to give him a good run. I'd be surprised if we didn't back him throughout the rest of the (test) cycle,” he told a virtual press conference.
“I'm very confident that he’s going to come good, whether it's in the first test match or the second, but I think we've got a good one for the future in the South African setup.”
Conrad said Stubbs’ technique was the major factor in giving him the job and his imposing size.
“Because you're going to be facing the new ball the bulk of the time, I know Tristan ticks all of those boxes. He's also quite an imposing character, a big strong boy, strapping boy. And I quite like that. I like the fact that at the top of the order we will imposing guys who have got a good aura about them with strong body language.
“But ultimately, the proof is going to be in the tasting. But yeah, I'm going down this road, and I'm confident we begin to reap the rewards.”
South Africa are playing a first test series since sending a second-string side to New Zealand in February and suffering two heavy defeats. They take on a Windies team who lost a three-test series in England last month.
“They've got three tough test matches under the belt and they'll come into this series at home taking a lot of confidence from several good performances,” Conrad said of the opposition.