Strachan informed the Celtic skipper he would lead out his country for the first time against Estonia on Wednesday, just moments before the manager and captain's press conference was due to start.
Brown, who will win his 30th cap in the Pittodrie friendly, said: "He just told me that I was captain and walked away and left me to my own wee moment. 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."
He added: "He kept it quiet, I was wondering why I was coming downstairs and the only one sitting in reception. 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."
Brown was given the armband in the continued absence of Manchester United midfielder Darren Fletcher, who is recovering from surgery to treat a chronic bowel condition, and after Wigan defender Gary Caldwell returned south with a minor injury.
Strachan, who signed Brown for Celtic in 2007, added: "He already knows what it's like to be a captain, a captain with pressure, and that made him favourite. He is also in fine form, and if you put that together that makes Scotty the captain for tomorrow."
Brown's public image is of a confrontational character on the park but Strachan stressed his true nature was much different.
"You know what he's like on the football field," he said. "I have never met anyone who has met Scott Brown who didn't think he was a good lad. Anyone who meets him thinks he is terrific.
"We were at Aberdeen Sports Village today, and I turned back and he was talking and laughing with the staff. They enjoyed his company. He is the same with the players, he is infectious, he has time for people.
"He has no time for anyone who wants to get the better of him on a football field, but that's fine. He is well respected as a player and a person in the squad."