Manager Gordon Strachan made the announcement on Tuesday, and the Celtic skipper, who will lead his country out for the first time at Pittodrie, said it is something he has dreamt about for years.
"He just told me that I was captain and walked away and left me to my own wee moment," Brown said.
"He kept it quiet, I was wondering why I was coming downstairs and the only one sitting in reception.
"He came up and told me and it was a great moment.
"It's a huge honour, a thing you dream of when you're younger, captaining Scotland.
"I've been lucky enough to do it for Celtic for the last couple of seasons and now to get the chance for this game for Scotland is a great honour."
The 27-year-old, who has been playing with a hip problem all season, did not train with the rest of the squad on Tuesday after snowfall moved their session indoors, but he is hopeful of playing for as long as possible on Wednesday.
"We have played a lot of games in the last month and training indoors wasn't the best for my body, so I did my own bit," Brown said.
"I only got 30 minutes at the weekend so I'm feeling fresh. I want to get as long as I can or as long as the gaffer wants to keep me on the park."
The former Hibernian player, who was signed by Strachan for Celtic in 2007, is also relishing returning to action under the new manager.
Brown said: "It's been great, it's been a good few years but he is the same old gaffer. He enjoys coming into work and he enjoys working with the lads, that's for sure."