Australian Scott Johnson is in charge of Scotland for the autumn Tests against Japan, South Africa and Australia, and next year's RBS 6 Nations championship.
But he will hand over the reins to Kiwi Cotter - once the 51-year-old's contract with French giants Clermont Auvergne ends next June - and then take up a director of rugby role with the Scottish Rugby Union.
Cotter has joined up with the squad ahead of Saturday's encounter with the Brave Blossoms as he bids to smooth the way for his arrival, but Brown does not believe his involvement will confuse the lines of command.
"There's no danger of that," he told Press Association Sport. "I know Scott and Vern have spoken a lot. They are very much on the same page about how they want to work and how they want to take Scotland forward. They will work very well as a team once Vern does arrive.
"Vern is really just here to observe but it is also good that he gets to meet the guys because it is a people business. If we get to know him and he gets to know us, that will help in the long run."
Meanwhile, SRU bosses have confirmed they have had to call in specialists after discovering a parasite living in the Murrayfield pitch.
The naturally occurring nematodes are known to damage the grass-root structure, but SRU groundstaff are already working on a solution and officials have stressed there is no chance of Saturday's match not going ahead.
SRU director of management services Mark Laidlaw said: "A soil examination in September revealed an excessive build-up of nematodes which have caused significant root damage.
"The results is a shallow and weakened root network and, though it continues to perform well in play, it can weaken under the significant pressure exerted by scrums.
"We've worked with some of the leading experts in this area to examine and treat one of the best surfaces in world rugby using natural remedies, including the spraying of garlic, but it takes a number of weeks to eradicate the problem and then to recover root strength.
"The groundstaff will continue their efforts to develop and consolidate the root structure, and hope to return the pitch to the standard we all expect to see at the national stadium."
- Sports & Recreation
- Clermont Auvergne