The Scottish Rugby Union confirmed Cotter's appointment on Sunday but he will not take over until June 2014, when his contract with Clermont Auvergne expires. The wait means Scott Johnson will have served 18 months as interim head coach when he steps aside to fully focus on his new role as SRU director of rugby.
"I think it's great. As we showed in the Six Nations we are a side on the up," Brown told Press Association Sport. "If you look at the teams he has been involved with, they are very strong. I'm sure when he comes in he will add a lot."
Cotter, 51, led Clermont to the European Challenge Cup in his first season in charge and the French title in 2010 after a hat-trick of second-placed finishes.
Brown added: "They (Clermont) are one of the top sides in Europe so for us to actually get a guy like that is exciting.
"As a player it's a massive boost that guys like that want to come and work with us. I'm sure he will add a lot to the squad."
SRU chief executive Mark Dodson said: "Vern is rightly regarded as one of the top coaches in the world and to have secured someone of his calibre is a coup for Scotland.
"He was our first choice as head coach and we are pleased to have secured him on a two-year contract taking us up to and beyond the Rugby World Cup 2015.
"We did our business with Vern some months ago and we believe we have the best man for the role with our national team. It's a measure of our standing that we have him on board."