The 26-year-old goalkeeper joins Birmingham at the start of July on a two-year deal when his current contract with Scottish side Motherwell expires.
Clark has also re-signed Irish keeper Colin Doyle and he will go head to head with Randolph for a starting place.
"Darren was somebody we monitored for a very long time, so we were delighted we were able to bring him in," said Clark.
"He had a fantastic time up in Scotland and he's still young. He obviously had other offers, certainly from other Championship clubs and potentially clubs higher, but we're happy he chose to come here.
"With the re-signing of Colin (Doyle) it means we're very strong in the goalkeeping department really early in the summer, so that's one area we can leave now."
Clark added: "Darren hasn't received a guarantee that he'll start.
"I said the same to both him and Colin that I want what you would class as two first team goalkeepers and it's up to them really, and then for me to decide.
"Basically they'll be given an opportunity over the course of pre-season and then we'll go from there."
"I'm now really settled with the two lads we've got and there is also young Nick Townsend who is coming through and doing extremely well for us."