Cotter is currently the head coach with French Top 14 club, Clermont Auvergne, who reached the Heineken Cup final earlier this month.
He has been with Clermont Auvergne since 2006, directing them to the French championship in 2010. Prior to his post in France, Cotter was part of the coaching set-up that steered Canterbury Crusaders to successive Super Rugby titles in 2005 and 2006.
"I believe this is a real coup for Scottish Rugby. Vern Cotter is a top rugby coach who is amongst the most highly-regarded coaches in the world," said Johnson.
"Until Vern arrives I will continue to lead Scotland as head coach and continue my duties as director of rugby."
Next season, Cotter will remain with Clermont but he is more than willing to play a supporting role until then.
Cotter said: "I'm absolutely thrilled and honoured to have been appointed to the role of Scotland head coach.
"Mark Dodson and the team at Scottish Rugby have a strategic vision and a determination to do something very special in the coming time and working with them and a talented group of players and coaches I look forward to the Scotland team growing in competitiveness and stature. We will build a winning team together.
"I very much look forward to joining Scotland and until I do permanently I will be on hand to support Scott and the coaches with any advice and support they need."