The 30-year-old Saracens back-row forward succeeds Edinburgh hooker Ross Ford as skipper and will lead the team out on the occasion of his 50th cap against the world champions on November 11.
Brown was in line for the role before a broken ankle forced him to miss this year's ill-fated RBS 6 Nations and the successful summer tour to Australia, Fiji and Samoa as Ford led the side throughout.
Now the former Glasgow Warriors player, who can play number eight or blindside flanker, will become Scotland's fifth captain in two years.
Robinson said: "Kelly Brown is an inspirational person. He has an aura, confidence and belief about him and a firm understanding of the game.
"He has been a very consistent performer for Scotland. It's because of these qualities that he has been appointed Scotland captain."
Robinson also praised Ford, who is in line to win his 62nd cap a week on Sunday.
"I would like to congratulate Ross Ford in the way he has handled himself as captain of the side but also in respect of Kelly taking over," Robinson added.
Brown's most recent Test appearance was in the Rugby World Cup defeat to Argentina in September 2011 which contributed to Scotland's pool stage exit for the first time.
Scrum-half Rory Lawson was captain that day and lock Alastair Kellock was skipper a week later against England before Ford assumed control, while scrum-half Mike Blair led Scotland in the most recent meeting with New Zealand, the 49-3 loss in November 2010.
Scrum-half Chris Cusiter, who is currently out injured, has also captained Scotland since Robinson's appointment in 2009.
Brown, who is from Melrose, made a try-scoring Scotland debut against Romania in 2005 and is renowned for his indomitable style.
Brown told www.scottishrugby.org: "It's obviously a huge honour and though I haven't played for Scotland for a while I'm really looking forward to the challenges ahead.
"On the flight up, it was like Christmas. It's been so long since I've actually played for Scotland so I'm really, really looking forward to that.
"And we're playing against the best side in the world so it's a massive, massive challenge but one, I'm sure, we'll thrive on."