"All the boys were very, very pleased for him," Smith said of Bromwich's appointment.
"To see him join our club in Melbourne as a young man, a 19-year-old I think he was, and to where he has come now in a short space of time, it's a credit to him.
"He's just going to go from strength to strength. You've seen over the past few years how much he has improved as a player on the field.
"He's played a few years in first grade and was happy to do his job but I think he realises now his capabilities and what he can actually do with a body his size.
For his part, Bromwich says actions will speak louder than words when it comes to his captaincy style.
"I've learnt a lot off Smithy but I'm my own man and I'll be looking at being myself and leading through my actions," he said.
Asked what his message would be to teammates before the Kiwis look to make it four Tests victories in a row against the Kangaroos, Bromwich said:
"It will be about protecting what Steve (Kearney) and the rest of the boys have built over the past two years. It will be along those lines. It's a big, important match for us and I'll be looking to lead from the front."
As for the prospect of Bromwich stealing any of Smith's captaincy methods, Kiwi coach Stephen Kearney couldn't resist having a little dig at the Aussie skipper.
"Gee, the ref will be in trouble," he quipped.